Relativistic Waves & Quantum Fields (RWQF | SPA7018U)

Year: 4 | Semester: A | Level: 7 | Credits: 15

Course organiser: Prof Gabriele Travaglini | Course deputy: Prof Steve Thomas

Synopsis:

This course provides a first introduction into the unification of last century's ground shaking revolutions in physics: Special Relativity and Quantum Mechanics. Relativistic wave equations for particles of various spins are derived and studied, and the physical interpretations of their solutions are analyzed. Students will learn about the fundamental concepts of quantum field theory, starting with classical field theory, quantisation of the free Klein-Gordon and Dirac field and the derivation of the Feynman propagator. Then interactions are introduced and a systematic procedure to calculate scattering amplitudes using Feynman diagrams is derived. As an example, some explicit tree-level scattering amplitudes for a scalar theory are calculated.

Aims:

This course provides a first introduction into the unification of last century's groundshaking revolutions in physics: Special Relativity and Quantum Mechanics.

Outcomes:

Students successfully completing this course will be able to analyze the relativistic wave equations for particles of various spins, and to discuss the physical interpretations of their basic solutions. They will become familiar with various concepts in classical field theory (Noether theorem, stress-energy tensor, symmetries and conserved currents) and quantum field theory (including canonical quantisation of the Klein-Gordon and Dirac fields, creation and annihilation operators, spin-statistics connection, commutators and time ordered products, the Feynman propagator).

Recommended books:

F. Mandl and G. Shaw, "Quantum Field Theory", J Wiley. (A pedagogical, clear book, the course will follow it as closely as possible. This book is also used in the 2nd term module Advanced Quantum Field Theory).