General Renormalization Theory

Classification of divergences

• Define the degree of divergence of the generic one-particel irreducible diagram
• Characterize renormalizable and non-renormalizable theories

Properties of divergences in renormalizable theories

• The possibility of removing all one-loop divergences in renormalizable theories is based on two facts:
  - the divergences are contained in a finite number of 1PI functions
  - the divergent part of a 1PI function is a polynomial in the external momenta
  Justify these two properties and explain how can be used in the renormalization program
• Describe the main difficulties arising in higher orders; what are the overlapping divergences?

Ward Identities and Unitarity

• Explain how the existence of a Hilbert space of physical states and of a unitary time evolution operator is guaranteed order by order in perturbation theory, in the Gupta-Bleuler formalism
  What is the crucial ingredient for the above properties?
• Give the definition of gauge anomaly