FYSS4515 Applied Quantum Field Theory (11 cr)

• Path-integral quantization and Feynman rules through discretization of space time

• Generating functionals and Feynman rules without discretization, effective action

• Symmetries in the path-integral language, Schwinger-Dyson equations, Ward identities

• Quantum anomalies, Adler-Bell-Jackiw anomaly, Adler-Bardeen theorem

• Path integral for gauge fields, Faddeev-Popov trick, ghost fields, Haar measure

• Systematics of renormalization, renormalization conditions, renormalized perturbation theory, renormalization schemes, renormalization of QED to one loop, 2-loop calculations

• Renormalization group equations and their solutions, beta functions, scale dependence of coupling constants and masses

• Wilson's approach to renormalization

• Quantum Chromodynamics, SU(3) symmetry, QCD Feynman rules, Bechhi-Rouet-Stora transformation, Slavnov-Tayloer identities, gauge invariance, renormalization of QCD to one loop, asymptotic freedom

• Weak interactions, electroweak Lagrangian density, Higgs mechanism, Goldstone theorem, quantization of weak interactions
  

After this course, the student will

• Understand the path-integral quantization and know how to use it to derive Feynman rules
  

• Understand more thoroughly the notion of renormalization
  

• Be able to apply renormalization methods to compute higher order corrections to scattering processes
  

• Understand the meaning, the origin, and how to calculate the scale dependencies of couplings and masses
  

• Understand the quantization of gauge fields and know how to apply them to scattering processes
  

• Understand the meaning of the effective action and effective potential and know how to compute quantum corrections to them

• Understand more deeply the quantization of electroweak theory and know how calculate observables predicted by the theory
  

• Understand the origin of quantum anomalies and their meaning
  

Lecture notes