- General introduction: Point particles to Fields, Long wave length approximation of harmonic lattice and phonons.
- Scalar Field Theory: Extension of quantum mechanics to relativistic particles, Klein-Gordon equation, Conservation laws, negative energy states, quantization of the scalar field and the Fock space, the Feynman propagator.
- Canonical Formalism: Lagrangian density, Symmetries, Noethers's theorem, Lorentz invariance, Gauge invariance.
- Dirac Field: Dirac Equation and Dirac algebra, Lorentz Transformations, Hole and Dirac sea, Time reversal and charge conjugation, Massless particles, Nonrelativistic limit and spin-orbit coupling, quantization of the Dirac field and the Pauli exclusion principle,the propagator.
- S-Matrix Theory: Interaction picture and adiabatic switching, S-matrix and scattering, Two point correlation function scalar and Dirac field this may be introduced in the context of free field theory as suggested above), time-ordered and normal products, the Dyson expansion and Wick's Theorem, Feynman rules for self interacting scalar theory.
- Electromagnetic field: Canonical formalism, quantization and gauge fixing, the propagator, the local gauge invariance and the covariant derivative, coupling to scalar and Dirac fields. Quantum electrodynamics, Feynman rules and simple applications.
- Applications: Klein paradox, vacuum fluctuation and Casimir effect, Lamb shift, anomalous magnetic moment, broken symmetry
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