MAU34401 Classical field theory
| Module Code | MAU34401 |
|---|---|
| Module Title | Classical field theory |
| Semester taught | Semester 1 |
| ECTS Credits | 5 |
| Module Lecturer | Prof. Andrei Parnachev |
| Module Prerequisites | MAU23402 Advanced classical mechanics II |
Assessment Details
- This module is examined in a 2-hour examination at the end of Semester 1.
- Continuous assessment contributes 20% towards the overall mark.
- Any failed components are reassessed, if necessary, by an exam in the reassessment session.
Contact Hours
11 weeks of teaching with 3 lectures per week.
Learning Outcomes
On successful completion of this module, students will be able to
- Apply standard methods to solve problems in electrostatics and magnetostatics.
- Describe how to find the equation of motion for a scalar field using a given Lagrangian density.
- Calculate the stress tensor and evaluate its divergence, relating it to a conservation law.
- Employ a variational principle to find the relativistic dynamics of a charged particle interacting with an electromagnetic potential.
- Use the Euler-Lagrange equation to show how a Lorentz scalar Lagrangian density with an interaction term leads to the Maxwell equations.
- Explain the concepts of gauge invariance and traceless tensor in the context of the stress tensor of a vector field.
- Demonstrate how the divergence of the symmetric stress tensor is related to the four-current density of an external source.
Module Content
- Electrostatics, Green's theorem, solution using Green functions.
- Spherically symmetric problems, magnetostatics.
- Maxwell equations, gauge invariance, transformation properties.
- Lorentz invariance; scalar, vector and tensor representations.
- Hamilton variational principle, Lagrangian for relativistic particle.
- Lorentz force, charged particle interaction, antisymmetric field tensor.
- Covariant field theory, tensors, scalar fields and the four-vector potential.
- Lagrangian density for a free vector field, symmetry properties.
- Canonical stress tensor; conserved, traceless and symmetric stress tensor.
- Particle and field energy-momentum and angular momentum conservation.
Recommended Reading
- Classical electrodynamics by J. David Jackson.
- Classical theory of fields by Landau and Lifshitz.
- Classical field theory by Francis E. Low.