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 non-relativistic quantum mechanical system, the propagator of a free particle, particle in a electromagnetic field, numerical simulation.