# FYSS4510 Quantum Field Theory (11 cr)

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## 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.

## Study materials

## Literature

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

## Completion methods

### Method 1

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### Method 2

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### Teaching (11 cr)

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Lectures, exercises and midterm exams.

#### Teaching

##### 9/6–11/29/2021 Lectures

##### 10/22–10/22/2021 Midterm

##### 12/3–12/3/2021 Midterm

##### 1/14–1/14/2022 Final exam

### Independent study (11 cr)

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Self-study, exercises and exam.