Symmetries: Definition, physical consequences of symmetries, Symmetries in Classical mechanics, Symmetries in Quantum mechanics, Heisenberg equations. Classical fields: Scalar fields, Gauge invariance, electromagnetism, energy and momentum tensor. Relativistic quantum mechanics: Klein Gordon equation, Dirac equation, introduction to second quantization Scattering theory: Green’s functions, asymptotic states, potential scattering, resonances Feynman path integrals: Classical action, transition amplitude of a nonrelativistic quantum mechanical system, the propagator of a free particle, particle in a electromagnetic field, numerical simulation.
