Description

This module reviews the most important concepts of theoretical physics, in particular: the action, symmetries, and conservation laws. It shows how they help physicists to think about seemingly disconnected topics, ranging from mechanics to quantum field theory. The module is recommended as an option for students who wish to specialise in theoretical physics, and who are intending to take level 7 theory option(s), such as PHYM013 Quantum Many-Body Theory. The topics covered will be also of interest to the students who want to understand the language of theoretical physics without making it their field of research.

Module Aims

Theoretical physics aims to organise our knowledge about the physical world using a compact set of principles that are expressed mathematically.

Intended Learning Outcomes (ILOs)

A student who has passed this module should be able to:

• Module Specific Skills and Knowledge:
  1. use symmetry principles to determine the form of the action of a physical system;
  2. derive equations of motion and conservation laws using the action;
  3. apply the concept of energy-stress tensor to a range of problems;
  4. describe the relation between least-action principle in classical theory and path integral approach in quantum theory;
  5. solve quantum-mechanical problems involving magnetic field;
  6. use the semiclassical approximation in quantum mechanics to solve problems;
• Discipline Specific Skills and Knowledge:
  7. apply the ideas and approaches of theoretical physics to a wide range of problems;
• Personal and Key Transferable / Employment Skills and Knowledge:
  8. devise a well-structured solution with clearly explained reasoning;
  9. use a range of resources in order to learn through independent study.

Syllabus Plan

1. Analytical dynamics
   least action principle, Euler-Lagrange equations, symmetries, Noether's theorem, conservation laws.
2. Relativistic mechanics
   geometry of space time, Lorentz symmetry, action, equations of motion, particle in external fields, scalar and vector potentials.
3. Classical field theory
   scalar field, its action and conservation laws, sound waves in gases and solids as an example.
4. Electromagnetic Fields
   Electromagnetic field tensor, action for electromagnetic field, Maxwell's equations, gauge invariance and charge conservation. Electromechanical analogy and the effective action.
5. Quantum theory
   Schrödinger equation and its Green function, Heisenberg representation, path integral formulation of quantum mechanics, path integral treatment of quantum harmonic oscillator
6. Semiclassical Methods
   Semiclassical approximation in quantum mechanics, the saddle point method.
7. Electromagnetic fields in quantum theory
   Gauge invariance, Aharonov-Bohm effect, Landau levels
8. Introduction to Quantum Field Theory
   Interactions mediated by virtual particles

Learning and Teaching

Learning Activities and Teaching Methods

Assessment

Resources

The following list is offered as an indication of the type & level of information that students are expected to consult. Further guidance will be provided by the Module Instructor(s).

Core text:

• Not applicable

Supplementary texts:

• Feynman R.P., Leighton R.B. and Sands M. (1963), Lectures on Physics, Vol. II, Addison-Wesley, ISBN 0-201-02117-X
• Feynman R.P. and Hibbs A.R. (1965), Quantum Mechanics and Path Integrals, McGraw Hill, ISBN 0-07-020650-3
• Goldstein H., Poole C. and Safko J. (2002), Classical Mechanics (3^rd edition), Addison Wesley, ISBN 0-201-65702-3
• Griffiths D.J. (2014), Introduction to Electrodynamics (4^th edition), Pearson Education, ISBN 978-0-321-85656-2
• Inkson J.C. (1984), Many Body Theory of Solids, Plenum, ISBN 0-306-41326-4
• Jackson J.D. (1998), Classical Electrodynamics (3^rd edition), Wiley, ISBN 0-471-30932-X
• Landau L.D. and Lifshitz E.M. (1975), Classical Theory of Fields (Vol. 2) (4^th edition), Butterworth-Heinemann, ISBN 978-0-750-62768-9
• Landau L.D. and Lifshitz E.M. (1976), Mechanics (Vol. 1) (3^rd edition), Butterworth-Heinemann, ISBN 978-0-750-62896-9
• Schiff L.I. (1968), Quantum mechanics (3^rd edition), McGraw-Hill, ISBN 0-070-55287-8
• Schwinger J., Deraad L.L., Milton K.A., Tsai W. and Norton J. (1998), Classical Electrodynamics, Perseus Books, ISBN 9-780-738200-56-9
• Shepherd P.J. (2013), A Course in Theoretical Physics, Wiley-Blackwell, ISBN 978-1-118-48134-9
• Ziman J.M. (1969), Elements of Advanced Quantum Theory, Cambridge University Press, ISBN 521-07458-4

ELE:

• http://newton.ex.ac.uk/redirects/ELE/phy3068

Further Information

Prior Knowledge Requirements

Re-assessment

Re-assessment is not available except when required by referral or deferral.

Notes: See Physics Assessment Conventions.

KIS Data Summary

Miscellaneous