Quantum Field Theory  

Summer term 2015, University of Giessen
Lecture: Mon 10:00-12:00 and Tue 14:00-16:00, SR 437

Exercise classes: Mon 12:00-13:00, 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, Gupta-Bleuler quantization

 
 
6)  Interactions and the S-matrix: interactions, Källén-Lehmann spectral representation, S-matrix, LSZ reduction formula, Green functions

 
 
7)  Perturbation theory: interaction picture, Wick theorem, Feynman diagrams, Feynman rules for n-point 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, two-body scattering processes

 
 
10)  QED: Lagrangian and gauge invariance, Feynman rules for fermions and photons, tree-level scattering amplitudes, cross sections, Coulomb potential

 
 
11)  Renormalization of QED: renormalized perturbation theory, fermion self-energy, 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)  Non-Abelian gauge theories: local gauge invariance, non-Abelian gauge theories, Faddeev-Popov quantization, QCD Feynman rules and perturbation theory

 
 

Literature

The course is mainly based on:

Further reading:


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