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Course on renormalization, taught in Pisa in 2015. (More chapters will be added later.)

Last update: May 9th 2015, 230 pages

Contents:

Preface

1. Functional integral

  • 1.1 Path integral
    • Schroedinger equation
    • Free particle
  • 1.2 Free field theory
  • 1.3 Perturbative expansion
    • Feynman rules
  • 1.4 Generating functionals, Schwinger-Dyson equations
  • 1.5 Advanced generating functionals
  • 1.6 Massive vector fields
  • 1.7 Fermions

2. Renormalization

  • 2.1 Dimensional regularization
    • 2.1.1 Limits and other operations in $D$ dimensions
    • 2.1.2 Functional integration measure
    • 2.1.3 Dimensional regularization for vectors and fermions
  • 2.2 Divergences and counterterms
  • 2.3 Renormalization to all orders
  • 2.4 Locality of counterterms
  • 2.5 Power counting
  • 2.6 Renormalizable theories
  • 2.7 Composite fields
  • 2.8 Maximum poles of diagrams
  • 2.9 Subtraction prescription
  • 2.10 Regularization prescription
  • 2.11 Comments about the dimensional regularization
  • 2.12 About the series resummation

3. Renormalization group

  • 3.1 The Callan-Symanzik equation
  • 3.2 Finiteness of the beta function and the anomalous dimensions
  • 3.3 Fixed points of the RG flow
  • 3.4 Scheme (in)dependence
  • 3.5 A deeper look into the renormalization group

4. Gauge symmetry

  • 4.1 Abelian gauge symmetry
  • 4.2 Gauge fixing
  • 4.3 Non-Abelian global symmetry
  • 4.4 Non-Abelian gauge symmetry

5. Canonical gauge formalism

  • 5.1 General idea behind the canonical gauge formalism
  • 5.2 Systematics of the canonical gauge formalism
  • 5.3 Canonical transformations
  • 5.4 Gauge fixing
  • 5.5 Generating functionals
  • 5.6 Ward identities

6. Quantum electrodynamics

  • 6.1 Ward identities
  • 6.2 Renormalizability of QED to all orders

7 Non-Abelian gauge field theories

  • 7.1 Renormalizability of non-Abelian gauge theories to all orders
    • Raw subtraction

A. Notation and useful formulas

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Book

14B1 D. Anselmi
Renormalization

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Last update: May 9th 2015, 230 pages

Contents: Preface | 1. Functional integral | 2. Renormalization | 3. Renormalization group | 4. Gauge symmetry | 5. Canonical formalism | 6. Quantum electrodynamics | 7. Non-Abelian gauge field theories | Notation and useful formulas | References

Course on renormalization, taught in Pisa in 2015. (More chapters will be added later.)