A three-semester subject sequence on quantum field theory stressing the relativistic quantum field theories relevant to the physics of the Standard Model. 8.323 is a one-semester self-contained subject in quantum field theory. Concepts and basic techniques are developed through applications in elementary particle physics and condensed matter physics. Includes the basic tools of field theory required for phenomenological studies. Topics: Functional integral formulation of quantum mechanics and many-particle systems. Classical field theory, symmetries, and Noether's theorem. Quantization of scalar fields. Feynman graphs, analytic properties of amplitudes and unitarity of the S-matrix. Renormalization and renormalization group. Spinors and the Dirac equation. Quantization of Dirac fields. Supersymmetry. Quantization of abelian gauge fields. Calculations in quantum electrodynamics. Classical Yang-Mills fields. The Higgs phenomenon and a description of the Standard Model. 8.324 is the second term of the quantum field theory sequence. Develops in depth some of the topics discussed in 8.323 and introduces some advanced material. Topics: Quantization of nonabelian gauge theories. BRST symmetry. Perturbation theory anomalies. Renormalization and symmetry breaking. The renormalization group. Critical exponents and scalar field theory. Conformal field theory. 8.325 is the third and last term of the quantum field theory sequence. Its aim is the proper theoretical discussion of the physic
A three-semester subject sequence on quantum field theory stressing the relativistic quantum field theories relevant to the physics of the Standard Model. 8.323 is a one-semester self-contained subject in quantum field theory. Concepts and basic techniques are developed through applications in elementary particle physics and condensed matter physics. Includes the basic tools of field theory required for phenomenological studies. Topics: Functional integral formulation of quantum mechanics and many-particle systems. Classical field theory, symmetries, and Noether's theorem. Quantization of scalar fields. Feynman graphs, analytic properties of amplitudes and unitarity of the S-matrix. Renormalization and renormalization group. Spinors and the Dirac equation. Quantization of Dirac fields. Supersymmetry. Quantization of abelian gauge fields. Calculations in quantum electrodynamics. Classical Yang-Mills fields. The Higgs phenomenon and a description of the Standard Model. 8.324 is the second term of the quantum field theory sequence. Develops in depth some of the topics discussed in 8.323 and introduces some advanced material. Topics: Quantization of nonabelian gauge theories. BRST symmetry. Perturbation theory anomalies. Renormalization and symmetry breaking. The renormalization group. Critical exponents and scalar field theory. Conformal field theory. 8.325 is the third and last term of the quantum field theory sequence. Its aim is the proper theoretical discussion of the physic
The strong force which bind quarks together is described by a relativistic quantum field theory called quantum chromodynamics (QCD). Subject surveys: The QCD Langrangian, asymptotic freedom and deep inelastic scattering, jets, the QCD vacuum, instantons and the U(1) problem, lattice guage theory, and other phases of QCD. 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.
Study of condensed matter systems where interactions between electrons play an important role. Topics vary depending on lecturer but may include low-dimension magnetic and electronic systems, disorder and quantum transport, magnetic impurities (the Kondo problem), quantum spin systems, the Hubbard model and high temperature superconductors. Topics are chosen to illustrate the application of diagrammatic techniques, field theory approaches, and renormalization group methods in condensed matter physics. In this course we shall develop theoretical methods suitable for the description of the many-body phenomena, such as Hamiltonian second-quantized operator formalism, Greens functions, path integral, functional integral, and the quantum kinetic equation. The concepts to be introduced include, but are not limited to, the random phase approximation, the mean field theory (aka saddle-point, or semiclassical approximation), the tunneling dynamics in imaginary time, instantons, Berry phase, coherent state path integral, renormalization group.
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