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PC4602 Relativistic quantum physics

Mike Birse

Email: mike.birse@man.ac.uk

This course draws together two of the key ideas from 20th century physics: special relativity and quantum mechanics. Combining these provides a framework for describing the interactions of particles at high energies or short distances. This framework, quantum field theory, underpins all our current theories of particle physics as well as much of nuclear and atomic physics.

As well as having a very wide scope, relativistic quantum mechanics is, as we shall see, much more complicated than the familiar nonrelativistic version. A first course like this has to be very selective. In it we shall focus on the general features of the framework, using simple examples to illustrate the range of physics which it can describe. The aim is to give you a flavour of the power of the principles of relativity and quantum mechanics when they are combined into quantum field theory. (This is not a course on the "nuts and bolts" of calculations in field theory nor on "stamp collecting" of particles and forces.)

Note that this document refers the course given in 2002-2004. In 2005 the course will be lectured by Graham Shaw.

Prerequisites

The only prerequisites for this course are quantum mechanics to the level of a book like Gasiorowicz, and introductory special relativity. Some background in classical relativistic electrodynamics would be helpful but is not essential. Other theoretical ideas and techniques--Lagrangian dynamics, Green's functions and complex variables--will not be required, although you will find them useful if you wish to learn more about quantum field theory beyond the level of this course. Good mathematical skills are essential.

Brief outline

  1. Relativistic wave equations
    Klein-Gordon equation
    Dirac equation
    Positive- and negative energy solutions
    Symmetries
    Conserved currents
    Interactions with EM fields
    Particle in a spherical potential
    The MIT bag model

  2. Quantum fields and their dynamics
    Klein-Gordon field
    Dirac field
    Antiparticles
    Feynman propagator
    Interaction picture and the S-matrix
    Covariant perturbation theory
    Feynman diagrams and rules
    Decay processes

  3. Scattering processes
    Exchange of virtual particles
    Cross sections
    Scattering of charged particles
    e-e+ annihilation
    High-energy scattering
    Form factors
    Deep-inelastic scattering and partons

A list of recommended textbooks can be found below. The detailed course structure gives references to relevant sections of these books.




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Mike Birse 2004-06-25