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MMath&Phys Mathematics and Physics
Year of entry: 2023
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Course unit details:
Gauge Theories (M)
|Unit level||Level 4|
|Teaching period(s)||Semester 2|
|Available as a free choice unit?||No|
Gauge Theories (M)
|Unit title||Unit code||Requirement type||Description|
|Quantum Field Theory (M)||PHYS40481||Pre-Requisite||Compulsory|
To understand in detail the origin and nature of the fundamental interactions generated by invariance of the Lagrangian under local gauge transformations.
1. use concepts of a Lie Algebra and Lie Groups in explaining symmetry properties in physics
2. use the principle of gauge invariance and generalize it from the Abelian theory of Quantum Electrodynamics to the non-Abelian cases of Quantum Chromodynamics and the Standard
Model (SM) of electroweak interactions
3. describe in detail the Higgs mechanism as a means to generate masses for the SM fermions, gauge bosons, and the observed Higgs boson, as well as the role of Yukawa interactions in explaining lepton- and quark-mixing phenomena in electroweak processes
4. explain the ideas and concepts involved in the motivation and construction of theories beyond the SM, including Grand Unified Theories
1. Preliminaries (2 lectures)
Abelian gauge invariance, Quantum Electrodynamics (QED);
QED Feynman rules.
2. Group Theory (4 lectures)
Lie groups; SO(N) and SU(N) Groups; Group representations
3. Quantum Chromodynamics (QCD) (6 lectures)
Non-Abelian gauge invariance; Fadeev-Popov Ghosts;
Becchi-Rouet-Stora Transformations; QCD Fenyman Rules;
Asymptotic Freedom and Confinement.
4. The Standard Model (SM) of Electroweak Interactions (8 lectures)
Goldstone Theorem; Higgs Mechanism; Yukawa Interactions; Quark and Lepton Mixing;
SM Feynam Rules, Unitarity and renormalizability of the SM.
5. Beyond the Standard Model (4 lectures)
Grand Unification and Supersymmetry
Fedback will be available on students’ individual written solutions to examples sheets, 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.
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.
|Scheduled activity hours|
|Assessment written exam||1.5|
|Independent study hours|
|Apostolos Pilaftsis||Unit coordinator|