Quantum Field Theory
Summer term 2015, University of Giessen
Lecture: Mon 10:0012:00 and Tue 14:0016:00, SR 437
Exercise classes: Mon 12:0013:00, SR 511 (Walter Heupel, Paul Walbott)
Topics
0)  Introduction: Standard Model, units and notation, special relativity, why QFT? 
1)  Classical scalar fields: classical field theory, real and complex scalar fields, symmetries, Noether theorem, Noether currents and charges 
2)  Quantization of scalar fields: field quantization, Hamiltonian and momentum operator, Fock space, antiparticles, Poincaré algebra and Heisenberg EoMs, causality and propagators 
3)  Dirac field: representations of the Lorentz group, Clifford algebra and spinors, Dirac Lagrangian and classical solutions, symmetries and currents 
4)  Quantization of the Dirac field: Hamiltonian and anticommutators, Fock space and Fermi statistics, causality and propagators, discrete symmetries

5)  Electromagnetic field: Classical Maxwell equations and Lagrangian, symmetries and currents, gauge fixing, GuptaBleuler quantization 
6)  Interactions and the Smatrix: interactions, KällénLehmann spectral representation, Smatrix, LSZ reduction formula, Green functions 
7)  Perturbation theory: interaction picture, Wick theorem, Feynman diagrams, Feynman rules for npoint functions and scattering amplitudes 
8)  Loops and renormalization: regularization techniques, renormalization and renormalization schemes, renormalizability 
9)  Cross sections and decay rates: cross section and decay rate formulas, twobody scattering processes 
10)  QED: Lagrangian and gauge invariance, Feynman rules for fermions and photons, treelevel scattering amplitudes, cross sections, Coulomb potential 
11)  Renormalization of QED: renormalized perturbation theory, fermion selfenergy, vacuum polarization, running coupling, vertex correction and anomalous magnetic moment 
12)  Path integrals: path integrals in QM and scalar QFT, generating functionals and perturbation theory, connected and 1PI diagrams, path integrals for fermions and Grassmann variables 
13)  NonAbelian gauge theories: local gauge invariance, nonAbelian gauge theories, FaddeevPopov quantization, QCD Feynman rules and perturbation theory 
Literature
The course is mainly based on:
 Maggiore, A Modern Introduction to Quantum Field Theory, Oxford 2005.
 Peskin and Schroeder, An Introduction to Quantum Field Theory, Perseus 1995.
 Weigand, Quantum Field Theory, lecture notes, Heidelberg 2013.
Further reading:
 Weinberg, Quantum Field Theory I + II, Cambridge 1995.
 Itzykson and Zuber, Quantum Field Theory, McGrawHill 1980.
 Huang, Quantum Field Theory: From Operators to Path Integrals, Wiley 2004.
 Srednicki, Quantum Field Theory, Cambridge 2007.
 Kaku, Quantum Field Theory: A Modern Introduction, Oxford 1993.
 Ryder, Quantum Field Theory, Cambridge 1996.
 Banks, Modern Quantum Field Theory: A Concise Introduction, Cambridge 2008.
 Haag, Local Quantum Physics: Fields, Particles, Algebras, Springer 1996.
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