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

Knowledge of the content of **PHY424** and **PHY646** is essential to follow this course.

Goal: To cover advanced field theoretic methods and a selection of special topics in subareas of Theoretical High Energy Physics.

- Renormalization of gauge theories. Power counting for spinors and vectors. Renormalization of Yukawa theory and QED. Current conservation and Ward identities.
- Anomalies. ABJ anomalies and gauge theory consistency. Accidental and approximate symmetries of the Standard Model. Chiral symmetry breaking and properties of pions and kaons.
- Path Integrals and Functional Methods. Schwinger-Dyson equations. 1PI and Wilson effective actions. Effective potential. Faddeev-Popov quantization of Yang-Mills theories. Ghosts. BRST symmetry. Renormalization of Yang-Mills Higgs. Asymptotic freedom and confinement. Anomalies and functional measure. Wess-Zumino-Witten theory.

- M. Peskin and D. Schroeder, Introduction to Quantum Field Theory, (Westview Press), 1995.
- M. Srednicki, Quantum Field Theory, (Cambridge University Press), 2007.
- R. J. Rivers, Path Integral Methods in Quantum Field Theory, (Cambridge University Press), 1987.
- S. Weinberg, Quantum Theory of Fields, Volume 1,2,3 (Cambridge University Press), 1996.
- 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/.

- Beyond the Standard Model, See-saw mechanism, Models for neutrino masses, Left-Right Symmetric Model, Pati-Salam Model. SU(5), SO(10) Grand Unification, Fermion masses in GUTs.
- Supersymmetry: Four and two component notation, Supersymmetry algebras, Supermultiplets and superfields. Gauge-invariant actions for chiral superfields. Supersymmetric gauge theories. Broken supersymmetry and Witten index. Spontaneous supersymmetry breaking at tree level. Supergravity basics, Gravity-mediated supersymmetry breaking. Supersymmetric LR models and GUTs.

- J. Wess and J. Bagger: Superymmetry and Supergravity (Princeton University Press), 1992.
- R. N. Mohapatra, Unification and Supersymmetry, (Springer), 2003.
- S. P. Martin, A Supersymmetry Primer Perspectives on Supersymmetry, pp 1-98, (World Scientific), 1998, https://arxiv.org/abs/hep-ph/9709356

- Lattice Field Theory: Scalar fields on the lattice, Markov Chain Monte Carlo, Metropolis algorithm, Statistical and systematic errors, Abelian and non-abelian gauge theories, Gauge-invariant observables, Scaling and continuum limit, Nielsen-Ninomiya theorem, Fermions on the lattice, Lattice Quantum Chromodynamics, Algorithms for fermions, Finite density and the sign problem, Lattice supersymmetry, Large-N gauge theories.
- Extended Field Configurations: Topology in field theory, Topological solitons and instantons, `t Hooft-Polyakov monopole, Instantons in Yang-Mills theories, U(1) problem, B, L violation by EW instantons, Theta angle and strong CP problem, Fluctuations around extended field configurations, Vacuum decay.

- C. Gattringer and C. B. Lang, Quantum Chromodynamics on the Lattice: An
Introductory Presentation, (Springer), 2010.
- T. Degrand and C. DeTar, Lattice Methods for Quantum Chromodynamics, (World
Scientific), 2006.
- H. J. Rothe, Lattice Gauge Theories: An Introduction, (World Scientific), 2005.

- Deep inelastic scattering of Leptons and Hadrons. Parton model and Parton distribution functions. Bjorken scaling. Sum rules. Scaling violation. Factorization and Hard processes. Elementary processes in QCD. Renormalization schemes, Renormalization of composite operators, Operator Product Expansion. Infrared divergences, KLN theorem and IR safe observables, Resummation, Parton shower and Monte-Carlo event generators, Elements of next-to-leading order QCD corrections.

- F. Halzen and A. D. Martin, Quarks & Leptons: An Introductory Course in Modern Particle Physics, (Wiley India), 2008.
- M. E. Peskin and D. V. Schroeder, An Introduction to Quantum Field Theory, (Westview Press), 1995.
- R. K. Ellis, B. R. Webber, W. J. Stirling, QCD and Collider Physics, (Cambridge University Press), 2003.
- R. D. Field, Applications of Perturbative QCD, (Basic Books), 1989.
- T. Muta, Foundations of Quantum Chromodynamics: An Introduction to Perturbative Methods in Gauge Theories, (World Scientific), 2009.