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18.238 Geometry and Quantum Field Theory (MIT) 18.238 Geometry and Quantum Field Theory (MIT)

Description

Geometry and Quantum Field Theory, designed for mathematicians, is a rigorous introduction to perturbative quantum field theory, using the language of functional integrals. It covers the basics of classical field theory, free quantum theories and Feynman diagrams. The goal is to discuss, using mathematical language, a number of basic notions and results of QFT that are necessary to understand talks and papers in QFT and String Theory. Geometry and Quantum Field Theory, designed for mathematicians, is a rigorous introduction to perturbative quantum field theory, using the language of functional integrals. It covers the basics of classical field theory, free quantum theories and Feynman diagrams. The goal is to discuss, using mathematical language, a number of basic notions and results of QFT that are necessary to understand talks and papers in QFT and String Theory.

Subjects

perturbative quantum field theory | perturbative quantum field theory | classical field theory | classical field theory | free quantum theories | free quantum theories | Feynman diagrams | Feynman diagrams | Renormalization theory | Renormalization theory | Local operators | Local operators | Operator product expansion | Operator product expansion | Renormalization group equation | Renormalization group equation | classical | classical | field | field | theory | theory | Feynman | Feynman | diagrams | diagrams | free | free | quantum | quantum | theories | theories | local | local | operators | operators | product | product | expansion | expansion | perturbative | perturbative | renormalization | renormalization | group | group | equations | equations | functional | functional | function | function | intergrals | intergrals | operator | operator | QFT | QFT | string | string | physics | physics | mathematics | mathematics | geometry | geometry | geometric | geometric | algebraic | algebraic | topology | topology | number | number | 0-dimensional | 0-dimensional | 1-dimensional | 1-dimensional | d-dimensional | d-dimensional | supergeometry | supergeometry | supersymmetry | supersymmetry | conformal | conformal | stationary | stationary | phase | phase | formula | formula | calculus | calculus | combinatorics | combinatorics | matrix | matrix | mechanics | mechanics | lagrangians | lagrangians | hamiltons | hamiltons | least | least | action | action | principle | principle | limits | limits | formalism | formalism | Feynman-Kac | Feynman-Kac | current | current | charges | charges | Noether?s | Noether?s | theorem | theorem | path | path | integral | integral | approach | approach | divergences | divergences | functional integrals | functional integrals | fee quantum theories | fee quantum theories | renormalization theory | renormalization theory | local operators | local operators | operator product expansion | operator product expansion | renormalization group equation | renormalization group equation | mathematical language | mathematical language | string theory | string theory | 0-dimensional QFT | 0-dimensional QFT | Stationary Phase Formula | Stationary Phase Formula | Matrix Models | Matrix Models | Large N Limits | Large N Limits | 1-dimensional QFT | 1-dimensional QFT | Classical Mechanics | Classical Mechanics | Least Action Principle | Least Action Principle | Path Integral Approach | Path Integral Approach | Quantum Mechanics | Quantum Mechanics | Perturbative Expansion using Feynman Diagrams | Perturbative Expansion using Feynman Diagrams | Operator Formalism | Operator Formalism | Feynman-Kac Formula | Feynman-Kac Formula | d-dimensional QFT | d-dimensional QFT | Formalism of Classical Field Theory | Formalism of Classical Field Theory | Currents | Currents | Noether?s Theorem | Noether?s Theorem | Path Integral Approach to QFT | Path Integral Approach to QFT | Perturbative Expansion | Perturbative Expansion | Renormalization Theory | Renormalization Theory | Conformal Field Theory | Conformal Field Theory | algebraic topology | algebraic topology | algebraic geometry | algebraic geometry | number theory | number theory

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18.238 Geometry and Quantum Field Theory (MIT)

Description

Geometry and Quantum Field Theory, designed for mathematicians, is a rigorous introduction to perturbative quantum field theory, using the language of functional integrals. It covers the basics of classical field theory, free quantum theories and Feynman diagrams. The goal is to discuss, using mathematical language, a number of basic notions and results of QFT that are necessary to understand talks and papers in QFT and String Theory.

Subjects

perturbative quantum field theory | classical field theory | free quantum theories | Feynman diagrams | Renormalization theory | Local operators | Operator product expansion | Renormalization group equation | classical | field | theory | Feynman | diagrams | free | quantum | theories | local | operators | product | expansion | perturbative | renormalization | group | equations | functional | function | intergrals | operator | QFT | string | physics | mathematics | geometry | geometric | algebraic | topology | number | 0-dimensional | 1-dimensional | d-dimensional | supergeometry | supersymmetry | conformal | stationary | phase | formula | calculus | combinatorics | matrix | mechanics | lagrangians | hamiltons | least | action | principle | limits | formalism | Feynman-Kac | current | charges | Noether?s | theorem | path | integral | approach | divergences | functional integrals | fee quantum theories | renormalization theory | local operators | operator product expansion | renormalization group equation | mathematical language | string theory | 0-dimensional QFT | Stationary Phase Formula | Matrix Models | Large N Limits | 1-dimensional QFT | Classical Mechanics | Least Action Principle | Path Integral Approach | Quantum Mechanics | Perturbative Expansion using Feynman Diagrams | Operator Formalism | Feynman-Kac Formula | d-dimensional QFT | Formalism of Classical Field Theory | Currents | Noether?s Theorem | Path Integral Approach to QFT | Perturbative Expansion | Renormalization Theory | Conformal Field Theory | algebraic topology | algebraic geometry | number theory

License

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18.366 Random Walks and Diffusion (MIT) 18.366 Random Walks and Diffusion (MIT)

Description

Mathematical modeling of diffusion phenomena: Central limit theorems, the continuum limit, first passage, persistence, continuous-time random walks, Levy flights, fractional calculus, random environments, advection-diffusion, nonlinear diffusion, free-boundary problems. Applications may include polymers, disordered media, turbulence, diffusion-limited aggregation, granular flow, and derivative securities. Mathematical modeling of diffusion phenomena: Central limit theorems, the continuum limit, first passage, persistence, continuous-time random walks, Levy flights, fractional calculus, random environments, advection-diffusion, nonlinear diffusion, free-boundary problems. Applications may include polymers, disordered media, turbulence, diffusion-limited aggregation, granular flow, and derivative securities.

Subjects

Discrete and continuum modeling of diffusion processes in physics | Discrete and continuum modeling of diffusion processes in physics | chemistry | chemistry | and economics | and economics | central limit theorems | central limit theorems | ontinuous-time random walks | ontinuous-time random walks | Levy flights | Levy flights | correlations | correlations | extreme events | extreme events | mixing | mixing | renormalization | renormalization | and percolation | and percolation

License

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8.323 Relativistic Quantum Field Theory I (MIT) 8.323 Relativistic Quantum Field Theory I (MIT)

Description

8.323, Relativistic Quantum Field Theory I, is a one-term self-contained subject in quantum field theory. Concepts and basic techniques are developed through applications in elementary particle physics, and condensed matter physics. 8.323, Relativistic Quantum Field Theory I, is a one-term self-contained subject in quantum field theory. Concepts and basic techniques are developed through applications in elementary particle physics, and condensed matter physics.

Subjects

Classical field theory | Classical field theory | symmetries | symmetries | and Noether's theorem. Quantization of scalar fields | and Noether's theorem. Quantization of scalar fields | spin fields | spin fields | and Gauge bosons. Feynman graphs | and Gauge bosons. Feynman graphs | analytic properties of amplitudes and unitarity of the S-matrix. Calculations in quantum electrodynamics (QED). Introduction to renormalization. | analytic properties of amplitudes and unitarity of the S-matrix. Calculations in quantum electrodynamics (QED). Introduction to renormalization.

License

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8.325 Relativistic Quantum Field Theory III (MIT) 8.325 Relativistic Quantum Field Theory III (MIT)

Description

This course is the third and last term of the quantum field theory sequence. Its aim is the proper theoretical discussion of the physics of the standard model. Topics include: quantum chromodynamics; the Higgs phenomenon and a description of the standard model; deep-inelastic scattering and structure functions; basics of lattice gauge theory; operator products and effective theories; detailed structure of the standard model; spontaneously broken gauge theory and its quantization; instantons and theta-vacua; topological defects; introduction to supersymmetry. This course is the third and last term of the quantum field theory sequence. Its aim is the proper theoretical discussion of the physics of the standard model. Topics include: quantum chromodynamics; the Higgs phenomenon and a description of the standard model; deep-inelastic scattering and structure functions; basics of lattice gauge theory; operator products and effective theories; detailed structure of the standard model; spontaneously broken gauge theory and its quantization; instantons and theta-vacua; topological defects; introduction to supersymmetry.

Subjects

gauge symmetry | gauge symmetry | confinement | confinement | renormalization | renormalization | asymptotic freedom | asymptotic freedom | anomalies | anomalies | instantons | instantons | zero modes | zero modes | gauge boson and Higgs spectrum | gauge boson and Higgs spectrum | fermion multiplets | fermion multiplets | CKM matrix | CKM matrix | unification in SU(5) and SO(10) | unification in SU(5) and SO(10) | phenomenology of Higgs sector | phenomenology of Higgs sector | lepton and baryon number violation | lepton and baryon number violation | nonperturbative (lattice) formulation | nonperturbative (lattice) formulation

License

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8.851 Strong Interactions: Effective Field Theories of QCD (MIT) 8.851 Strong Interactions: Effective Field Theories of QCD (MIT)

Description

This is a course in the construction and application of effective field theories, which are the modern tool of choice in making predictions based on the Standard Model. Concepts such as matching, renormalization, the operator product expansion, power counting, and running with the renormalization group will be discussed. Topics will be taken from factorization in hard processes relevant for the LHC, heavy quark decays and CP violation, chiral perturbation theory, non-relativistic bound states in field theory (QED and QCD), nucleon effective theories with a fine-tuning, and possibly other subjects from QCD, electroweak physics, and gravity. This is a course in the construction and application of effective field theories, which are the modern tool of choice in making predictions based on the Standard Model. Concepts such as matching, renormalization, the operator product expansion, power counting, and running with the renormalization group will be discussed. Topics will be taken from factorization in hard processes relevant for the LHC, heavy quark decays and CP violation, chiral perturbation theory, non-relativistic bound states in field theory (QED and QCD), nucleon effective theories with a fine-tuning, and possibly other subjects from QCD, electroweak physics, and gravity.

Subjects

matching | matching | renormalization | renormalization | the operator product expansion | the operator product expansion | power counting | power counting | heavy quark decays | heavy quark decays | CP violation | CP violation | factorization in hard processes | factorization in hard processes | non-relativistic bound states in field theory (QED and QCD) | non-relativistic bound states in field theory (QED and QCD) | chiral perturbation theory | chiral perturbation theory | few-nucleon systems | few-nucleon systems

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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18.366 Random Walks and Diffusion (MIT) 18.366 Random Walks and Diffusion (MIT)

Description

This graduate-level subject explores various mathematical aspects of (discrete) random walks and (continuum) diffusion. Applications include polymers, disordered media, turbulence, diffusion-limited aggregation, granular flow, and derivative securities. This graduate-level subject explores various mathematical aspects of (discrete) random walks and (continuum) diffusion. Applications include polymers, disordered media, turbulence, diffusion-limited aggregation, granular flow, and derivative securities.

Subjects

Discrete and continuum modeling of diffusion processes in physics | chemistry | and economics | Discrete and continuum modeling of diffusion processes in physics | chemistry | and economics | central limit theorems | central limit theorems | continuous-time random walks | continuous-time random walks | Levy flights | Levy flights | correlations | correlations | extreme events | extreme events | mixing | mixing | renormalization | renormalization | and percolation | and percolation | percolation | percolation

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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18.366 Random Walks and Diffusion (MIT) 18.366 Random Walks and Diffusion (MIT)

Description

This graduate-level subject explores various mathematical aspects of (discrete) random walks and (continuum) diffusion. Applications include polymers, disordered media, turbulence, diffusion-limited aggregation, granular flow, and derivative securities. This graduate-level subject explores various mathematical aspects of (discrete) random walks and (continuum) diffusion. Applications include polymers, disordered media, turbulence, diffusion-limited aggregation, granular flow, and derivative securities.

Subjects

Discrete and continuum modeling of diffusion processes in physics | chemistry | and economics | Discrete and continuum modeling of diffusion processes in physics | chemistry | and economics | central limit theorems | central limit theorems | continuous-time random walks | continuous-time random walks | Levy flights | Levy flights | correlations | correlations | extreme events | extreme events | mixing | mixing | renormalization | renormalization | and percolation | and percolation | percolation | percolation

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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8.325 Relativistic Quantum Field Theory III (MIT) 8.325 Relativistic Quantum Field Theory III (MIT)

Description

This is the third and last term of the quantum field theory sequence. The course is devoted to the standard model of particle physics, including both its conceptual foundations and its specific structure, and to some current research frontiers that grow immediately out of it. This is the third and last term of the quantum field theory sequence. The course is devoted to the standard model of particle physics, including both its conceptual foundations and its specific structure, and to some current research frontiers that grow immediately out of it.

Subjects

gauge symmetry | gauge symmetry | confinement | confinement | renormalization | renormalization | asymptotic freedom | asymptotic freedom | anomalies | anomalies | instantons | instantons | zeromodes | zeromodes | gauge boson and Higgs spectrum | gauge boson and Higgs spectrum | fermion multiplets | fermion multiplets | CKM matrix | CKM matrix | unification in SU(5) andSO(10) | unification in SU(5) andSO(10) | phenomenology of Higgs sector | phenomenology of Higgs sector | lepton andbaryon number violation | lepton andbaryon number violation | nonperturbative (lattice)formulation | nonperturbative (lattice)formulation

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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8.323 Relativistic Quantum Field Theory I (MIT) 8.323 Relativistic Quantum Field Theory I (MIT)

Description

In 8.323, Relativistic Quantum Field Theory I, concepts and basic techniques are developed through applications in elementary particle physics, and condensed matter physics.Topics include: Classical field theory, symmetries, and Noether's theorem. Quantization of scalar fields and spin 1/2 fields. Interacting fields and Feynman diagrams. In 8.323, Relativistic Quantum Field Theory I, concepts and basic techniques are developed through applications in elementary particle physics, and condensed matter physics.Topics include: Classical field theory, symmetries, and Noether's theorem. Quantization of scalar fields and spin 1/2 fields. Interacting fields and Feynman diagrams.

Subjects

Quantum physics | Quantum physics | Classical field theory | Classical field theory | symmetries | symmetries | and Noether's theorem | and Noether's theorem | Quantization of scalar fields | Quantization of scalar fields | spin fields | spin fields | and Gauge bosons | and Gauge bosons | Feynman graphs | Feynman graphs | analytic properties of amplitudes and unitarity of the S-matrix | analytic properties of amplitudes and unitarity of the S-matrix | Calculations in quantum electrodynamics (QED) | Calculations in quantum electrodynamics (QED) | Introduction to renormalization | Introduction to renormalization

License

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8.334 Statistical Mechanics II: Statistical Physics of Fields (MIT) 8.334 Statistical Mechanics II: Statistical Physics of Fields (MIT)

Description

This is the second term in a two-semester course on statistical mechanics. Basic principles are examined in 8.334, such as the laws of thermodynamics and the concepts of temperature, work, heat, and entropy. Topics from modern statistical mechanics are also explored including the hydrodynamic limit and classical field theories. This is the second term in a two-semester course on statistical mechanics. Basic principles are examined in 8.334, such as the laws of thermodynamics and the concepts of temperature, work, heat, and entropy. Topics from modern statistical mechanics are also explored including the hydrodynamic limit and classical field theories.

Subjects

the hydrodynamic limit and classical field theories | the hydrodynamic limit and classical field theories | Phase transitions and broken symmetries: universality | Phase transitions and broken symmetries: universality | correlation functions | correlation functions | and scaling theory | and scaling theory | The renormalization approach to collective phenomena | The renormalization approach to collective phenomena | Dynamic critical behavior | Dynamic critical behavior | Random systems | Random systems

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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8.334 Statistical Mechanics II: Statistical Physics of Fields (MIT) 8.334 Statistical Mechanics II: Statistical Physics of Fields (MIT)

Description

Includes audio/video content: AV lectures. This is the second term in a two-semester course on statistical mechanics. Basic principles are examined in this class, such as the laws of thermodynamics and the concepts of temperature, work, heat, and entropy. Topics from modern statistical mechanics are also explored, including the hydrodynamic limit and classical field theories. Includes audio/video content: AV lectures. This is the second term in a two-semester course on statistical mechanics. Basic principles are examined in this class, such as the laws of thermodynamics and the concepts of temperature, work, heat, and entropy. Topics from modern statistical mechanics are also explored, including the hydrodynamic limit and classical field theories.

Subjects

the hydrodynamic limit and classical field theories | the hydrodynamic limit and classical field theories | Phase transitions and broken symmetries: universality | Phase transitions and broken symmetries: universality | correlation functions | correlation functions | and scaling theory | and scaling theory | The renormalization approach to collective phenomena | The renormalization approach to collective phenomena | Dynamic critical behavior | Dynamic critical behavior | Random systems | Random systems

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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8.851 Strong Interactions (MIT) 8.851 Strong Interactions (MIT)

Description

Strong Interactions is a course in the construction and application of effective field theories, which are a modern tool of choice in making predictions based on the Standard Model. Concepts such as matching, renormalization, the operator product expansion, power counting, and running with the renormalization group will be discussed. Topics will be taken from heavy quark decays and CP violation, factorization in hard processes (deep inelastic scattering and exclusive processes), non-relativistic bound states in field theory (QED and QCD), chiral perturbation theory, few-nucleon systems, and possibly other Standard Model subjects. Strong Interactions is a course in the construction and application of effective field theories, which are a modern tool of choice in making predictions based on the Standard Model. Concepts such as matching, renormalization, the operator product expansion, power counting, and running with the renormalization group will be discussed. Topics will be taken from heavy quark decays and CP violation, factorization in hard processes (deep inelastic scattering and exclusive processes), non-relativistic bound states in field theory (QED and QCD), chiral perturbation theory, few-nucleon systems, and possibly other Standard Model subjects.

Subjects

matching | matching | renormalization | renormalization | the operator product expansion | the operator product expansion | power counting | power counting | heavy quark decays | heavy quark decays | CP violation | CP violation | factorization in hard processes | factorization in hard processes | non-relativistic bound states in field theory (QED and QCD) | non-relativistic bound states in field theory (QED and QCD) | chiral perturbation theory | chiral perturbation theory | few-nucleon systems | few-nucleon systems | strong force | strong force | quarks | quarks | relativistic quantum field theory | relativistic quantum field theory | quantum chromodynamics | quantum chromodynamics | QCD | QCD | QCD Langrangian | QCD Langrangian | asymptotic freedom | asymptotic freedom | deep inelastic scattering | deep inelastic scattering | jets | jets | QCD vacuum | QCD vacuum | instantons | instantons | U(1) proglem | U(1) proglem | lattice gauge theory | lattice gauge theory | strong interactions | strong interactions | standard model | standard model | operator product expansion | operator product expansion | factorization | factorization | hard processes | hard processes | exclusive processes | exclusive processes | non-relativistic bound states | non-relativistic bound states | QED | QED | massive particles | massive particles | effective field theory | effective field theory | soft-collinear effective theory | soft-collinear effective theory

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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8.334 Statistical Mechanics II: Statistical Mechanics of Fields (MIT) 8.334 Statistical Mechanics II: Statistical Mechanics of Fields (MIT)

Description

This is the second term in a two-semester course on statistical mechanics. Basic principles are examined in 8.334, such as the laws of thermodynamics and the concepts of temperature, work, heat, and entropy. Topics from modern statistical mechanics are also explored including the hydrodynamic limit and classical field theories. This is the second term in a two-semester course on statistical mechanics. Basic principles are examined in 8.334, such as the laws of thermodynamics and the concepts of temperature, work, heat, and entropy. Topics from modern statistical mechanics are also explored including the hydrodynamic limit and classical field theories.

Subjects

the hydrodynamic limit and classical field theories | the hydrodynamic limit and classical field theories | Phase transitions and broken symmetries: universality | Phase transitions and broken symmetries: universality | correlation functions | and scaling theory | correlation functions | and scaling theory | The renormalization approach to collective phenomena | The renormalization approach to collective phenomena | Dynamic critical behavior | Dynamic critical behavior | Random systems | Random systems | correlation functions | correlation functions | and scaling theory | and scaling theory | Phase transitions and broken symmetries: universality | correlation functions | and scaling theory | Phase transitions and broken symmetries: universality | correlation functions | and scaling theory

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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8.334 Statistical Mechanics II (MIT) 8.334 Statistical Mechanics II (MIT)

Description

Topics from modern statistical mechanics are explored in 8.334, Statistical Mechanics II, including:The hydrodynamic limit and classical field theories.Phase transitions and broken symmetries: universality, correlation functions, and scaling theory.The renormalization approach to collective phenomena.Integrable models. Quantum phase transitions. Topics from modern statistical mechanics are explored in 8.334, Statistical Mechanics II, including:The hydrodynamic limit and classical field theories.Phase transitions and broken symmetries: universality, correlation functions, and scaling theory.The renormalization approach to collective phenomena.Integrable models. Quantum phase transitions.

Subjects

the hydrodynamic limit and classical field theories | the hydrodynamic limit and classical field theories | Phase transitions and broken symmetries: universality | correlation functions | and scaling theory | Phase transitions and broken symmetries: universality | correlation functions | and scaling theory | The renormalization approach to collective phenomena | The renormalization approach to collective phenomena | Dynamic critical behavior | Dynamic critical behavior | Random systems | Random systems

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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8.334 Statistical Mechanics II: Statistical Physics of Fields (MIT)

Description

This is the second term in a two-semester course on statistical mechanics. Basic principles are examined in 8.334, such as the laws of thermodynamics and the concepts of temperature, work, heat, and entropy. Topics from modern statistical mechanics are also explored including the hydrodynamic limit and classical field theories.

Subjects

the hydrodynamic limit and classical field theories | Phase transitions and broken symmetries: universality | correlation functions | and scaling theory | The renormalization approach to collective phenomena | Dynamic critical behavior | Random systems

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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8.851 Strong Interactions (MIT)

Description

Strong Interactions is a course in the construction and application of effective field theories, which are a modern tool of choice in making predictions based on the Standard Model. Concepts such as matching, renormalization, the operator product expansion, power counting, and running with the renormalization group will be discussed. Topics will be taken from heavy quark decays and CP violation, factorization in hard processes (deep inelastic scattering and exclusive processes), non-relativistic bound states in field theory (QED and QCD), chiral perturbation theory, few-nucleon systems, and possibly other Standard Model subjects.

Subjects

matching | renormalization | the operator product expansion | power counting | heavy quark decays | CP violation | factorization in hard processes | non-relativistic bound states in field theory (QED and QCD) | chiral perturbation theory | few-nucleon systems | strong force | quarks | relativistic quantum field theory | quantum chromodynamics | QCD | QCD Langrangian | asymptotic freedom | deep inelastic scattering | jets | QCD vacuum | instantons | U(1) proglem | lattice gauge theory | strong interactions | standard model | operator product expansion | factorization | hard processes | exclusive processes | non-relativistic bound states | QED | massive particles | effective field theory | soft-collinear effective theory

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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8.334 Statistical Mechanics II: Statistical Mechanics of Fields (MIT)

Description

This is the second term in a two-semester course on statistical mechanics. Basic principles are examined in 8.334, such as the laws of thermodynamics and the concepts of temperature, work, heat, and entropy. Topics from modern statistical mechanics are also explored including the hydrodynamic limit and classical field theories.

Subjects

the hydrodynamic limit and classical field theories | Phase transitions and broken symmetries: universality | correlation functions | and scaling theory | The renormalization approach to collective phenomena | Dynamic critical behavior | Random systems | correlation functions | and scaling theory | Phase transitions and broken symmetries: universality | correlation functions | and scaling theory

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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18.366 Random Walks and Diffusion (MIT)

Description

This graduate-level subject explores various mathematical aspects of (discrete) random walks and (continuum) diffusion. Applications include polymers, disordered media, turbulence, diffusion-limited aggregation, granular flow, and derivative securities.

Subjects

Discrete and continuum modeling of diffusion processes in physics | chemistry | and economics | central limit theorems | continuous-time random walks | Levy flights | correlations | extreme events | mixing | renormalization | and percolation | percolation

License

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8.334 Statistical Mechanics II (MIT)

Description

Topics from modern statistical mechanics are explored in 8.334, Statistical Mechanics II, including:The hydrodynamic limit and classical field theories.Phase transitions and broken symmetries: universality, correlation functions, and scaling theory.The renormalization approach to collective phenomena.Integrable models. Quantum phase transitions.

Subjects

the hydrodynamic limit and classical field theories | Phase transitions and broken symmetries: universality | correlation functions | and scaling theory | The renormalization approach to collective phenomena | Dynamic critical behavior | Random systems

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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18.366 Random Walks and Diffusion (MIT)

Description

Mathematical modeling of diffusion phenomena: Central limit theorems, the continuum limit, first passage, persistence, continuous-time random walks, Levy flights, fractional calculus, random environments, advection-diffusion, nonlinear diffusion, free-boundary problems. Applications may include polymers, disordered media, turbulence, diffusion-limited aggregation, granular flow, and derivative securities.

Subjects

Discrete and continuum modeling of diffusion processes in physics | chemistry | and economics | central limit theorems | ontinuous-time random walks | Levy flights | correlations | extreme events | mixing | renormalization | and percolation

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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8.334 Statistical Mechanics II: Statistical Physics of Fields (MIT)

Description

This is the second term in a two-semester course on statistical mechanics. Basic principles are examined in 8.334, such as the laws of thermodynamics and the concepts of temperature, work, heat, and entropy. Topics from modern statistical mechanics are also explored including the hydrodynamic limit and classical field theories.

Subjects

the hydrodynamic limit and classical field theories | Phase transitions and broken symmetries: universality | correlation functions | and scaling theory | The renormalization approach to collective phenomena | Dynamic critical behavior | Random systems

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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8.334 Statistical Mechanics II: Statistical Physics of Fields (MIT)

Description

This is the second term in a two-semester course on statistical mechanics. Basic principles are examined in this class, such as the laws of thermodynamics and the concepts of temperature, work, heat, and entropy. Topics from modern statistical mechanics are also explored, including the hydrodynamic limit and classical field theories.

Subjects

the hydrodynamic limit and classical field theories | Phase transitions and broken symmetries: universality | correlation functions | and scaling theory | The renormalization approach to collective phenomena | Dynamic critical behavior | Random systems

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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8.323 Relativistic Quantum Field Theory I (MIT)

Description

8.323, Relativistic Quantum Field Theory I, is a one-term self-contained subject in quantum field theory. Concepts and basic techniques are developed through applications in elementary particle physics, and condensed matter physics.

Subjects

Classical field theory | symmetries | and Noether's theorem. Quantization of scalar fields | spin fields | and Gauge bosons. Feynman graphs | analytic properties of amplitudes and unitarity of the S-matrix. Calculations in quantum electrodynamics (QED). Introduction to renormalization.

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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18.366 Random Walks and Diffusion (MIT)

Description

This graduate-level subject explores various mathematical aspects of (discrete) random walks and (continuum) diffusion. Applications include polymers, disordered media, turbulence, diffusion-limited aggregation, granular flow, and derivative securities.

Subjects

Discrete and continuum modeling of diffusion processes in physics | chemistry | and economics | central limit theorems | continuous-time random walks | Levy flights | correlations | extreme events | mixing | renormalization | and percolation | percolation

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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