This course is an introduction to perturbative relativistic quantum field theory, for scalars, fermions, and gauge fields, in both the canonical and path integral formulations.
The course begins with a review of relativistic wave equations. It introduces the Lagrangian formulation for classical fields and then discusses the canonical quantisation of free fields with spins 0, 1/2 and 1. An outline is given of perturbation theory for interacting fields and Feynman diagram methods for Quantum Electrodynamics are introduced. The course also introduces path integral methods in quantum field theory. This gives a better understanding of the quantisation of gauge theories and forms an essential tool for the understanding and development of the 'standard model' of particle physics. Topics include: Path integral formalism, Feynman rules, LSA formalism, loop diagrams and regularisation and renormalization of divergencies.

**Lecturer:** Dino Jaroszynski, M Wiggins, B Ersfeld, G Vieux

**Institution:** Strathclyde

**Hours Equivalent Credit: **8

**Assessment:** Continuous Assessment

This course is cross-listed with the Particle Physics Theme

**Course Summary**

Particle accelerators are a valuable tool in probing high-energy physics (up to the Large Hadron Collider at CERN) that is vital in helping us to understand the universe. They also have a wealth of more down-to-earth societal applications such as radiotherapy machines for treating cancer. This course gives a concise introduction to the field of conventional accelerators that use radio-frequency or microwave radiation in order to accelerate charged particles (electrons, protons, ions) to high energy.

The course will cover the following topics:

(i) overview and history of the accelerators and outlook for future advances including the development of laser-driven accelerators,

(ii) accelerator applications including medical imaging, isotope production and oncology,

(iii) RF accelerating cavities including waveguide propagation, superconducting cavities and power delivery,

(iv) beam line diagnostics for characterising beam parameters such as charge, transverse profile, energy spread and emittance,

(v) transverse and longitudinal beam dynamics outlining beam parameters and transport and the effect of beam quality on transport and focusing,

(vi) non-linear beam dynamics including resonances, betatron motion and beam instabilities,

(vii) electromagnetic radiation emitted by relativistic charged particles due to their acceleration: synchrotron and betatron,

(viii) radiation damping and application of such radiation.

**Lecturers:** Kenneth Wraight, Dima Maneuski and Andrew Blue

**Lab heads:** Stephan Eisenhardt (Edinburgh) and Richard Bates (Glasgow)

**Institutions: **Glasgow & Edinburgh

**Hours Equivalent Credit:** 16 (11 lectures, 1x2hr lab & 1x3hr Lab)

**Assessment:** Assignment sheets

**Course Summary**

**(11 lectures, 1x2hr lab & 1x3hr Lab)**

**Lecturer: Christoph Englert**

**Institution: **Glasgow

**Hours Equivalent Credit: **20

**Assessment: **Open book exam

**Common Core **Joint Master’s & PhD course

**Course Summary**

The course will cover the following topics: classical Lagrangian field theory, Lorentz covariance of relativistic field equations, quantisation of the Klein- Gordon, Dirac and electromagnetic fields, interacting fields, Feynman diagrams, S-matrix expansion and calculating all lowest order scattering amplitudes and cross sections in Quantum Electrodynamics (QED).

Assessment: Take-home exam (Glasgow). Closed-book exam (Edinburgh).

**Lecturer: **Einan Gardi

**Institution: **Edinburgh

**Hours Equivalent Credit:** 22

**Assessment: **Take-home exam OR project and presentation

Joint Master’s and PhD course delivered by** lectures at the University of Edinburgh**.

(Non-Edinburgh students are welcome to attend the lectures in Edinburgh in person)

**Course Summary**

The course introduces path integral methods in quantum field theory. This modern approach (as opposed to canonical quantisation) allows the relatively simple quantisation of gauge theories and forms an essential tool for the understanding and development of the ‘standard model’ of particle physics. Topics include: Path integral formalism, Feynman rules, LSZ formalism, loop diagrams and divergencies, regularisation and renormalisation.

• Path Integrals for quantum mechanics and quantum field theory, Green’s functions and generating functionals for free scalar fields

• Interacting scalar fields, Feynman rules/diagrams, connected and one-particle-irreducible Green’s functions

• Spectral functions, in/out states, reduction formulae (LSZ formal-ism), S-matrix

• One loop Feynman diagrams for scalar theories, divergencies, dimensional regularisation, renormalisation, renormalisation group, beta- and gamma- functions, Landau poles, infra-red and ultra-violet fixed points

• Path integrals for fermions, Grassmann variables, Yukawa interactions