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Module Catalogue

Throughout the 2021-22 academic year, we will be prioritising face to face teaching as part of a blended learning approach that builds on the lessons learned over the course of the Coronavirus pandemic. Teaching will vary between online and on-campus delivery through the year, and you should read guidance from the academic department for details of how this will work for a particular module. You can find out more about the University’s overall response to Coronavirus at: https://warwick.ac.uk/coronavirus.

PX430-7.5 Gauge Theories for Particle Physics

Department
Physics
Level
Undergraduate Level 4
Module leader
Bill Murray
Credit value
7.5
Module duration
5 weeks
Assessment
100% exam
Study location
University of Warwick main campus, Coventry

Introductory description

The electromagnetic field is a gauge field. Gauge changes to the vector potential (Aμ → Aμ - ∂μ Φ with Φ an arbitrary function of position and time), combined with multiplication of the wavefunction of particles with charge q by the phase factor, exp( iqΦ) , leave all physical properties unchanged. This is called a gauge symmetry. In particle physics, this idea is generalized to (space- and time-dependent) unitary matrix-valued fields multiplying spinor wavefunctions and fields. This generalization of the theory of an electron in an electromagnetic field is the basis for current theories of elementary particles.

The module starts with the theory of the electron in the electromagnetic field making the gauge symmetry explicit. It then discusses the gauge symmetries appropriate for the various theories and approximate theories used to describe other elementary particles and their interactions with their corresponding gauge fields.

Module aims

To develop ideas used in gauge theories and apply these to the field of particle physics. To describe the theory underpinning the Standard Model of Particle Physics should and to highlight the symmetry properties of the theory. To consider Quantum Electrodynamics (QED) in some detail, and to illustrate its success by comparison with experiments.

Outline syllabus

This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.

1. Introduction and revision: relativistic quantum mechanics and notation; the Klein Gordon equation; the Dirac equation and interpretation of negative energy solutions; quantum numbers and spin; revision of matrices, Hermitan, unitary, determinants
2. Group theory: definition of a group, examples of discrete groups; continuous groups, Lie groups, examples: U(1), SU(2), SU(3)
3. Gauge invariance: symmetries and conservation laws; current conservation; Noether's theorem; the gauge principle; examples: Maxwell's equations, quantum electrodynamics
4. Quantum field theories: brief outline of the deeper theory; Feynman rules and diagrams
Non Abelian gauge theories: SU(2) and the electroweak interaction; SU(3) and QCD; local nonAbelian gauge theory; gauge fields; self-interaction
5. Quantum electrodynamics: perturbation theory; scattering and cross sections
Learning outcomes

By the end of the module, students should be able to:

• Explain the theoretical framework of the Standard Model
• Explain the symmetry properties associated with gauge invariance
• Calculate amplitudes for simple QED processes
• Discuss qualitatively properties of the strong and weak interactions
Indicative reading list

Gauge Theories in Particle Physics, I.J.R.Aitchison and A.J.G.Hey, IOP Publishing

Subject specific skills

Knowledge of mathematics and physics. Skills in modelling, reasoning, thinking

Transferable skills

Analytical, communication, problem-solving, self-study

Study time

Type Required
Lectures 15 sessions of 1 hour (20%)
Private study 60 hours (80%)
Total 75 hours
Private study description

Working through lecture notes, solving problems, wider reading, discussing with others taking the module, revising for exam, practising on past exam papers

Costs

No further costs have been identified for this module.

You must pass all assessment components to pass the module.

Assessment group B2
Weighting Study time
On-campus Examination 100%

Answer 2 questions

• Answerbook Green (8 page)
• Students may use a calculator
Feedback on assessment

Personal tutor, group feedback

Courses

This module is Optional for:

• TMAA-G1PE Master of Advanced Study in Mathematical Sciences
• Year 1 of G1PE Master of Advanced Study in Mathematical Sciences
• Year 1 of G1PE Master of Advanced Study in Mathematical Sciences
• Year 1 of TMAA-G1P9 Postgraduate Taught Interdisciplinary Mathematics
• Year 1 of TMAA-G1PD Postgraduate Taught Interdisciplinary Mathematics (Diploma plus MSc)
• Year 1 of TMAA-G1P0 Postgraduate Taught Mathematics
• Year 1 of TMAA-G1PC Postgraduate Taught Mathematics (Diploma plus MSc)
• Year 4 of UPXA-F304 Undergraduate Physics (BSc MPhys)
• Year 4 of UPXA-F303 Undergraduate Physics (MPhys)

This module is Option list A for:

• Year 1 of TMAA-G1P0 Postgraduate Taught Mathematics
• Year 3 of UMAA-G100 Undergraduate Mathematics (BSc)
• Year 4 of UMAA-G101 Undergraduate Mathematics with Intercalated Year

This module is Option list B for:

• Year 4 of UPXA-FG33 Undergraduate Mathematics and Physics (BSc MMathPhys)
• Year 4 of UPXA-FG31 Undergraduate Mathematics and Physics (MMathPhys)

This module is Option list C for:

• UMAA-G105 Undergraduate Master of Mathematics (with Intercalated Year)
• Year 3 of G105 Mathematics (MMath) with Intercalated Year
• Year 5 of G105 Mathematics (MMath) with Intercalated Year
• UMAA-G103 Undergraduate Mathematics (MMath)
• Year 3 of G103 Mathematics (MMath)
• Year 4 of G103 Mathematics (MMath)
• UMAA-G106 Undergraduate Mathematics (MMath) with Study in Europe
• Year 3 of G106 Mathematics (MMath) with Study in Europe
• Year 4 of G106 Mathematics (MMath) with Study in Europe