**[Cr:4, Lc:4, Tt:0, Lb:0]**

Knowledge of the content of **PHY424** is essential to follow this course.

Goal: To complete the introduction of all basic tools required for computation and interpretation of observables in High Energy Physics.

- Functional methods and Observables: Generating functionals, Vacuum bubbles, and Connected Green's functions, Combinatorics from functional differentiation, Exact propagator and its spectral decomposition, Functional differentiation for fermionic fields, S matrix and LSZ formula, Feynman rules for scattering amplitudes, Scattering cross-section and Decay rate calculations.
- QED and U(1) gauge invariance: Photon propagator and gauge fixing, Feynman rules for QED, QED processes.
- Lie groups and Lie algebras: Unitary and orthogonal groups and their representations, Tensor methods, Non-abelian covariant derivative and field strength, gauge invariant action, Feynman rules for non-abelian theories.
- Spontaneous symmetry breaking: Goldstone theorem and Higgs mechanism, Unitary and R-xi gauges and massive vector propagators,
- Standard Model: Spontaneously broken chiral gauge theory, CKM mixing and charged Lepton masses, B, L symmetries of SM masses, Feynman rules for SM, Effective current current Fermi theory, Meson and Baryon currents, Pion decay constant, Propagator for unstable particles, FEYNCALC, FEYNRULES and MADGRAPH for automated tree calculation, Weinberg d=5 operator and neutrino masses, Neutrino oscillations.
- Loop diagrams in scalar QFT: Wick rotation, Feynman parameters and dimensional regularization, Passarino-Veltman functions and use of tables thereof, Power counting, BPHZ renormalization of phi + phi theory, Running mass and pole mass, anomalous dimensions, Running couplings, Renormalization Group and necessity use of running couplings.

- M. E. Peskin and D. Schroeder, Introduction to Quantum Field Thoery, (Westview Press), 1995.
- M. Srednicki, Quantum Field Theory, (Cambridge university Press), 2007.
- R. J. Rivers, Path Integral Methods in Quantum Field Thoery, (Cambridge university Press), 1988.
- A. Lahiri and P. B. Pal, A First Book of Quantum Field Thoery, (Narosa), 2007.
- T. P. Cheng and L. F. Li, Gauge Theory of Elementary Particle Physics, (Oxford University Press), 1988.
- L. H. Ryder, Quantum Field Theory, (Cambridge University Press), 1996.
- T. Goto, Formulae for Supersymmetry, MSSM and More, http://research.kek.jp/people/tgoto/