# MPhys Physics

Year of entry: 2021

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## Course unit details:Quantum Field Theory (M)

Unit code PHYS40481 10 Level 4 Semester 1 Department of Physics & Astronomy No

### Overview

Quantum Field Theory

### Pre/co-requisites

Unit title Unit code Requirement type Description
Lagrangian Dynamics PHYS20401 Pre-Requisite Recommended
Electrodynamics (M) PHYS30441 Pre-Requisite Recommended
Advanced Quantum Mechanics PHYS40202 Pre-Requisite Recommended

PHYS40682 - Gauge Theories

### Aims

To understand the unifying framework of quantization of fundamental forces and particles in agreement with special relativity.

### Learning outcomes

This course unit detail provides the framework for delivery in 21/22 and may be subject to change due to any additional Covid-19 impact.  Please see Blackboard / course unit related emails for any further updates
On completion successful students will be able to:
1. Explain the concept of canonical quantization for scalar, vector and fermion fields.
2. Explain the concept of global and local symmetries in Quantum Field Theory and their
implications
3. Derive the Feynman rules from the Lagrangian formalism, use these to calculate S-matrix
elements, and understand their physical significance.
4. Calculate the lifetime of unstable particles and cross sections of reactions that occur in the
lowest order of perturbation theory.
5. Explain the concept of renormalization and apply this to field theories.

### Syllabus

1. Preliminaries           (3 Lectures)
Classical Lagrangian Dynamics; Lagrangian Field Theory; Global and Local Symmetries; Noether's Theorem.

2. Canonical Quantization                        (4 lectures)
From Classical to Quantum Mechanics; Quantum Fields and Causality; Canonical Quantization of Scalar Field Theory; Complex Fields and Anti-Particles.

3. The S-Matrix in Quantum Field Theory                     (5  lectures)
Time Evolution of Quantum States and the S-Matrix; Feynman Propagator and Wick's Theorem; Transition Amplitudes and Feynman Rules; Particle Decays and Cross Sections; Unitarity and the Optical Theorem.

4. Quantum Electrodynamics        (6  lectures)
Dirac Spinors;  Quantization of the Fermion Field;  Gauge Symmetry;  Quantization of the Electromagnetic Field;  the Photon Propagator and Gauge Fixing;  Feynman Rules for Quantum Electrodynamics.

5. Renormalization                          (6 lectures)
Renormalizability; Dimensional Regularization, Renormalization of a Scalar Theory; Anomalous magnetic moment and the Lamb shift.

### Assessment methods

Method Weight
Written exam 100%

### Feedback methods

Feedback will be available on students’ individual written solutions to selected examples, which will be marked, and model answers will be issued.

Cheng, T. P. and Li, L. F. Gauge Theory of Elementary Particle Physics, Oxford  University
Press, 1984.
Mandl, F. and Shaw, G. Quantum Field Theory, Wiley, 1992.
Peskin, M. E. and Schroeder, D. V. Quantum Field Theory, Perseus Books Group, 1995.
Pokorski, S. Gauge Field Theories, Cambridge University Press, 2000, Second Edition.

### Study hours

Scheduled activity hours
Assessment written exam 1.5
Lectures 24
Independent study hours
Independent study 74.5

### Teaching staff

Staff member Role
Mrinal Dasgupta Unit coordinator