Lagrangian density formalism of Lorentz scalar, Dirac and Weyl spinor, and vector gauge fields. Action variations, symmetries, conservation laws. Canonical quantization, Fock space. Interacting local fields, temporal evolution. Wicks theorem, propagators, and vertex functions, Feynman rules and diagrams. Scattering S matrix examples with tree level amplitudes. Path quantization. 1-loop intro to renormalization.
Course Summary: the quantum many-body problem and its the conceptual formulation in terms of functional integrals, the basics of perturbative calculations at both zero and non-zero temperature, mean field theory and its interpretation as a saddle point of a functional integral, fluctuations including collective modes, the field theory of linear response and transport calculations and the new features associated with nonequilibrium physics.
Quantum optics, including: quantiziation of the electromagnetic field, open quantum systems, light-matter interaction, coherent control, collective phenomena, measurement theory and decoherence, and applications in quantum information science.
Prerequisites: PHYS E6081 or the instructors permission. Semiclassical and quantum mechanical electron dynamics and conduction; dielectric properties of insulators; semiconductors; defects; magnetism; superconductivity; low-dimensional structures; soft matter.
Prerequisites: PHYS G6092. This course will study the classical field theories used in electromagnetism, fluid dynamics, plasma physics, and elastic solid dynamics. General field theoretic concepts will be discussed, including the action, symmetries, conservation laws, and dissipation. In addition, classical field equations will be analyzed from the viewpoint of macroscopic averaging and small-parameter expansions of the fundamental microscopic dynamics. The course will also investigate the production and propagation of linear and nonlinear waves; with topics including linearized small-amplitude waves, ordinary and extraordinary waves, waves in a plasma, surface waves, nonlinear optics, wave-wave mixing, solitons, shock waves, and turbulence.
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Prerequisites: PHYS G6037-G6038. Basic aspects of particle physics, focusing on the Standard Model.