# FYSS4510 Quantum Field Theory (11 cr)

Study level:
0-5
Language:
English
Responsible organisation:
Department of Physics
Curriculum periods:
2020-2021, 2021-2022, 2022-2023

## Description

• Basics of classical field theory – Noether’s theorem and conservation laws

• Quantization of free real scalar field

• Scalar propagators

• Complex scalar field

• Dirac equation, its plane-wave solutions and their Lorentz transformations

• Quantization of the free Dirac field

• Dirac propagators

• Discrete symmetries in quantum field theory

• Pictures in quantum mechanics

• Perturbative expansion of correlation functions

• Wick’s theorem

• Feynman diagrams

• Scatterin cross sections and the scattering matrix

• Yukawa theory

• Potential scattering

• Maxwell’s equation in covariant form and the gauge freedom

• Quantization of the free electromagnetic field in the Coulomb gauge

• Quantum electrodynamics in the Coulomb gauge

• Coulomb potential

• Gupta-Bleurer quantization in the Lorenz gauge

• Analytical structure of correlation functions

• Lehmann-Symanzik-Zimmerman reduction

• Optical theorem

• Unstable particles - decay width

• Basic processes in Quantum Electrodynamics

• High- and low-energy limits

• Crossing symmetry

• Bound states

• Braking radiation in Quantum Electrodynamics

• Virtual correction to electron-photon vertex

• Electron’s self-energy correction – mass renormalization

• Photon’s self-energy correction - charge renormalization and running coupling

• Pauli-Villars and dimensional regularization

• Basics of the path-integral method

## Learning outcomes

After completing this course the student knows how to

• Quantize free scalar theory, Dirac theory, and electromagnetism

• Form a perturbative series for interacting theories and derive their Feynman rules.

• Compute scattering cross sections

• Renormalize QED and scalar theory to one loop

## Description of prerequisites

• FYSS4300 Particle Physics
• FYSS7531-FYSS7532 Quantum Mechanics 2, parts A&B
• MATA200 Complex calculus/FYSS7301 Complex analysis

or similar.

Lecture notes

## Literature

• Peskin & Schroder, An introduction to Quantum Field theory, Westview Press, ISBN 0-201-50397-2.

## Completion methods

### Method 1

Description:
Given every other year, starting autumn 2021.
Evaluation criteria:
50% of point required for passing the course, for example exercises 40% and midterm exams 60%.
Time of teaching:
Period 1, Period 2
Select all marked parts

### Method 2

Description:
This completion method is for students for whom completion method 1 is not possible for specific reasons (e.g. language, distance learning, statement for special study arrangements). Contact the teacher before enrolling to the course via this completion method.
Evaluation criteria:
50% of point required for passing the course, for example exercises 40% and midterm exams 60%.
Select all marked parts
Parts of the completion methods
x

### Teaching (11 cr)

Type:
Participation in teaching
0-5
Evaluation criteria:
50% of point required for passing the course, for example exercises 40% and midterm exams 60%.
Language:
English
Study methods:

Lectures, exercises and midterm exams.

x

### Independent study (11 cr)

Type:
Independent study