Quantum Field Theory I

General Course Information

All details regarding location, schedule, and ECTS credits are available in the KSL

Course Description

This course constitutes the first semester of a two-semester introductory sequence in quantum field theory. It covers the following topics:

Part I: Quantum Field Theory (QFT) of the Scalar Field

• Canonical quantization of the free scalar field
• Wick's theorem and the scattering amplitude
• Feynman diagrams and Feynman rules for phi4 theory
• Example calculations of various scattering amplitudes
• Continuous symmetries in QFT
• Internal symmetries (continuous and discrete)

Part II: QFT of the Fermion Field

• Representations of the Lorentz groupT
• The Dirac Lagrangian and equation
• Clifford algebra and gamma matrices
• Canonical quantization of spinors
• Feynman rules

Part III: QFT of the Photon Field and Quantum Electrodynamics QED

• Canonical quantization of the electromagnetic field
• Coupling to fermions -> QED and its Feynman rules
• Coupling to scalars -> scalar QED (sQED) and its Feynman rules
• Calculation of simple processes in (s)QED
• Introduction to loop corrections and renormalization up to three-loop level

The exercise sessions and problem sets are an integral part of the course, as several essential concepts are developed there.

This course should be attended in parallel with "Exercices in Theoretical Physics" and prior to "Quantum Field Theory II" (Spring semester).

Students are requested to register for the course in advance via the KSL.

Further reading

Week 1

1. Preface of Weinberg QFT Vol. 1 book.

2. An article on the Cern Courier presenting the modern view of Effective Field Theories (here called "A Theory of Theories", and Chiral Perturbation Theory, developed here in Bern as "the mother of effective field theories")

3. H. Leutwyler's account of the history of strong interactions (first few sections should be easy to read, the rest probably not). This is part of the larger volume to celebrate 50 years of QCD: