MPhys Physics

This unit provides a comprehensive introduction to quantum field theory as applied to the Standard Model of particle physics. 

The unit aims to provide students with a detailed coverage of Gauge Field Theories including a knowledge of the gauge symmetry principle underlying the fundamental forces in the Universe.

It will familiarise the learner with the various gauge groups associated with the different parts of the Standard Model of particle physics and give an in-depth knowledge of the Higgs mechanism responsible for the generation of particle masses. An ability to be able to calculate basic scattering processes at colliders such as the LHC will be an outcome of the course. 

ILO 1

Formulate the path integral method for field quantization.

 

ILO 2

Apply the concept of symmetry groups to derive fundamental interactions via gauge symmetries.

 

ILO 3

Derive the specific features of a non-Abelian gauge field theory and in particular the case of strong interactions including the transformation properties of quarks, gluons and their interactions.

 

ILO 4

Apply the ideas behind renormalization to the gauge theories of the Standard Model, including derivation of key properties such as asymptotic freedom and confinement.

 

ILO 5

Formulate the origin of mass in the theories of the standard model via the Higgs mechanism, obtain the Feynman rules for the electroweak sector of the standard model and compute cross-sections for collider processes.

 

Syllabus (S2 30 lectures + 6 examples classes)  

1. Introduction and Preliminaries (4 Lectures). Introduction to path integral quantization. Abelian gauge invariance, QED Feynman rules.  

2. Group Theory (4 lectures). Lie groups, SO(N) and SU(N) groups. Group Representations.  

3. Non-abelian gauge invariance and QCD (3 lectures). Transformation of quark and gluon fields, Feynman rules for QCD, Fadeev Popov ghosts    

4. Renormalization, RG methods and lattice techniques (8 lectures). Recap of renormalization and dimensional regularization main concepts, renormalization group, running coupling and beta functions, asymptotic freedom and confinement, Anomalies, Introduction to lattice gauge theory.  

5. The Electroweak sector (8 lectures). Fermi and IVB theories and problems with unitarity and renormalizability, unified electroweak theory, Higgs mechanism, CKM matrix.  

6. Standard model summary, shortcomings and BSM (3 lectures). Standard model Feynman rules, calculations for collider processes, strong CP problem, evidence for BSM. 

Synchronous learning: lectures, example classes

 

Asynchronous learning: online material, collated on Canvas 

 

M. E. Peskin and D. V. Schroeder, Quantum Field Theory, Perseus Books Group, 1995.

S. Pokorski, Gauge Field Theories, Cambridge University Press, 2000, Second Edition. 

Tuition fees for home students will be £10,050 for the 2027/28 academic year. In England and Wales, tuition fees for home undergraduate students are subject to the Government fee cap, which the Government has announced will be £10,050 for the 2027/28 academic year.

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