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Instructor: Haralampos Panagopoulos


Symmetries: Definition, Types of symmetries, Physical consequences. Symmetries of Classical and Quantum Mechanics. Lorentz group, unitary groups. Noether's theorem.
Relativistic Quantum Mechanics: Klein-Gordon, Dirac equation. Relativistic spin. Relativistic study of hydrogen. Elements of second quantization.
Classical Fields: Action of Electromagnetism. Gauge symmetry. Non-Abelian fields. Energy-momentum tensor.
Introduction to the Standard Model: Coupling of fermions to gauge fields. Chiral Lagrangians. Coupling to the Higgs field. Spontaneous violation of gauge symmetry. CKM matrix.
Scattering theory: Green's functions. Asymptotic states. Potential scattering. Born approximation. Optical theorem. Partial wave analysis. Analytic properties of scattering amplitudes. Resonances.
Special topics in Perturbation Theory: Time-dependent perturbations. Radiation emission and absorption. Raman scattering.
Functional integrals: Heisenberg – Schrödinger pictures. The propagator as a sum over paths. The role of functional integrals in the quantum description of particles fields and strings. Computational methods for functional integrals.
Many-body systems: Atoms. Calculational methods. Hartree – Fock approximation.

Assesment: Homework sets: 10%,  Midterm exam: 30%,  Final exam: 60%.