Brief tentative yearly syllabus:
- Review of special theory of relativity.
- A short introduction to group theory.
- Lorentz and Poincare groups and their representations.
- Discrete symmetries of special relativity.
- Review of the structure and principles of quantum mechanics.
- Scattering and perturbation theories' general principles.
- A quick overview of canonical quantization prescription and
- The cluster decomposition principle.
- Pauli's principle.
- Creation and annihilation operators.
- Cluster decomposition and causality.
- Quantum fields and antiparticles.
- Causal massive scalar fields.
- Causal massive vector fields.
- Aspects of general causal fields.
- Masslessness and its issues.
- Quantum field theory of scalar fields.
- Vaccuum-to-vacuum amplitudes and Wick's theorem.
- Generator functions of amplitudes.
- Schwinger-Dyson equations.
- Quantum effective action and irreducible connected diagrams.
- Calculations on basic scattering and decay processes.
- Dimensional regularization of scalar quantum field theories and
renormalization procedure. Explicit calculations in one loop approximation.
- Path integral formalism and its applications to quantum field
- Quantization of free spin 1/2 particles.
- Issues on quantization of massless vector fields and gauge theories.
- Path integral quantization of spinor electrodynamics a la Fadeev and Popov, BRST symmetry.
- One loop renormalization of quantum electrodynamics via
- One loop predictions of quantum electrodynamics.
- Basic aspects of quantization of non-abelian gauge theories and BRST symmetries.
- Short introduction to the standard model of particle