The notions of a “field” and of a (quantum) field theory applied to various branches of classical and quantum physics. Energy and distance scales, units and conventions in particle physics. Uncertainty relations in the relativistic domain and the need for many-particle description.
Canonical quantization of the electromagnetic field in Coulomb gauge and the notion of its “quanta,” the photons. Applications: thermal blackbody radiation and Casimir energy.
General classical fields, their symmetries and conservation laws (Noether’s theorem). Dimensional analysis: marginal, relevant, and irrelevant terms in various dimensions.
Canonical quantization of real and complex scalar fields. Conserved quantities as quantum operators.
Symmetry realization, symmetry breaking, and Goldstone bosons. Application: the nonlinear sigma model describing the Higgs sector of the Standard Model and the low-energy chiral lagrangian of QCD.
Interacting fields: Feynman diagrams, the scattering matrix and cross section calculations. Decay widths and phase space.
Spin-1/2 fields: Spinor representations, Weyl and Dirac spinors, Dirac equation. Quantizing fermi fields and statistics.
Examples of tree-level processes in quantum electrodynamics.
(1) Lagrangian and Hamiltonian formulations of classical mechanics.
(2) Maxwell equations, energy and momentum of the electromagnetic fields, Lorentz invariance (special relativity).
(3) Nonrelativistic quantum mechanics, in particular, angular momentum theory will be relied upon.
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