Project IV 2025-26

Unification of Forces: Symmetries and Symmetry Breaking

Steve Abel and Andreas Braun

Description

The Standard Model of particle physics has been an astonishly succesful description of fundamental interactions, that had its last mayor prediction confirmed with the discovery of the Higgs boson. If you visit CERN you can go and buy a T-shirt with the Standard Model Lagrangian written on it. In this project we will explore what this equation means, how it is based on simple principles of symmetry, and how these symmetries can be extended.

After reviewing basic aspects of quantum field theory, gauge theories, and chiral fermions we can give a concise definition of what the Standard Model is and how it describes fundamental forces using symmetry. We will then continue with

  • Spontaneously broken (gauge) symmetry: this is a crucial ingredient in the Standard Model which also plays an important role in many other areas of physics.
  • Unification of forces. Using symmetries as a guiding principle, one may construct larger symmetries in which the ones we understand are combined and/or extended.

Pre and Co-requisites

MATH2071 Mathematical Physics II

MATH4061 Advanced Quantum Theory IV

(or comparable courses in physics)

Reading material

  • W.Greiner, 'Gauge Theory of Weak Interactions', Springer (2000)
  • M.Peskin, D. Schroeder,'Quantum Field Theory', CRC Press (1995)
  • S.Weinberg, 'The Quantum Theory of Fields, Vol II', Cambridge University Press (1995)
  • R. Barbieri, 'Lectures on the ElectroWeak Interactions' Springer (2007)
  • T.-P. Cheng, L.-F. Li, 'Gauge Theory of elementary particle physics', Oxford University Press (1988)
  • J. F. Donoghue, 'Dynamics of the Standard Model', Cambridge University Press (2014)