course dates credits
Quantum Field Theory I Oct 2 - Dec 14 3
teachers schedule term
Marco Serone 8:30 - 9:45 1


  • LSZ Reduction Formula and Kallen-Lehmann Representation
  • The Optical Theorem
  • General Renormalization Theory
  • Coleman-Weinberg Potential
  • Quantization and Ward Identities for QED
  • The Sliding Scale and the Summation of Leading Logs
  • Callan-Symanzik Renormalization Group equations
  • Scheme Dependence and Asymptotic Behaviours of Coupling Constants
  • RG Improved Effective Potential
  • Quantization of Non-Abelian Gauge Theories
  • BRST Symmetry
  • Background Field Method
  • Effective Field Theories
  • Naturalness and the Hierarchy Problem
  • Non-Leptonic Decays
  • (Ir)relevance of Higher Dimensional Operators
  • Spontaneously Broken Global Symmetries
  • Goldstone Theorem
  • Spontaneously Broken Gauge Symmetries
  • Higgs Mechanism
  • (*)Effective Field Theory for Broken Symmetries
  • (*)Mesons in QCD
  • (*)Anomalies from One-Loop Graphs
  • (*)Gauge Anomalies and Their Cancellation in the Standard Model
  • (*)Anomalous Breaking of Scale Invariance
  • Strong CP Problem and Axions
  • Large Orders in Perturbation Theory

An essential part of the course will be provided by several exercises to be solved. The exercises will concern the computation of Feynman graphs relevant for the course, their explicit renormalization, and various alternative techniques for field theory computations. The topics with (*) are optional for students in the Astroparticle curriculum.


  • Quantum Mechanics
  • Basic concepts of Quantum Field Theory
    (quantization of scalar, fermion and abelian gauge fields, Feynman rules, path integral formulation)


  • S. Weinberg, ''The Quantum Theory of Fields'', vol. I and II
  • M.E. Peskin and D.V. Schroeder, ''An Introduction to Quantum Field Theory''

Online Resources:

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