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Advanced Quantum Field Theory (QFT II)

Jan Martin Pawlowski, summer term 2023

Preliminary TeX version (pdf)

Editor: Jan M. Pawlowski

 
 

Table of Contents

 
  • 9 Functional integral approach
 
    • 9.1 Path integral in quantum mechanics
 
    • 9.2 Functional integral for scalar fields
 
    • 9.3 Feynman rules
 
    • 9.4 Effective action & spontaneous symmetry breaking
 
  • 10 Functional integral for fermions
 
    • 10.1 Quantum mechanics
 
    • 10.2 Quantum field theory
 
  • 11 Functional Methods
 
    • 11.1 Effective action
 
    • 11.2 Functional relations
 
  • 12 Non-Abelian gauge theories
 
    • 12.1 Action & gauge invariance
 
    • 12.2 Generating functional
 
    • 12.3 BRST-Symmetry & Unitarity
 
    • 12.4 Quantum master equation
 
    • 12.5 Gribov & Neuberger Problem: a one-dimensional example
 
  • 13 QCD
 
    • 13.1 Renormalisation
 
    • 13.2 Running Coupling
 
  • 14 Lattice gauge theory
 
    • 14.1 Scalar fields on the lattice
 
    • 14.2 Non-Abelian gauge fields on the lattice
 
    • 14.3 Wegner-Wilson loop & static quark potential
 
    • 14.4 Continuum limit of lattice Yang-Mills theory
 
    • 14.5 Fermions on the lattice
 
  • 15 Renormalisation group
 
    • 15.1 Wilson's renormalisation group
 
    • 15.2 Fixed points
 
    • 15.3 Callan-Symanzik equation
 
  • 16 Symmetry breaking in QFT
 
    • 16.1 Spontaneous symmetry breaking
 
    • 16.2 O(N) models
 
    • 16.3 Dynamical spontaneous symmetry breaking in QCD
 
    • 16.4 Anomalies and anomalous symmetry breaking
 
  • 17 A brief look at the Standard Model
 
    • 17.1 The gauge-Higgs sector
 
    • 17.2 Fermion interaction with gauge fields
 
    • 17.3 Higgs interactions
 
    • 17.4 Chiral fermions
 
    • 17.5 Beyond Standard Model physics
 
  • 18 Higgs mechanism
 
    • 18.1 Abelian Higgs model
 
    • 18.2 Non-Abelian Higgs