MAU34401 Classical field theory

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.
• The module is passed if the overall mark for the module is 40% or more. If the overall mark for the module is less than 40% and there is no possibility of compensation, the module will be reassessed as follows: 
  1) A failed exam in combination with passed continuous assessment will be reassessed by an exam in the supplemental session; 
  2) The combination of a failed exam and failed continuous assessment is reassessed by the supplemental exam; 
  3) A failed continuous assessment in combination with a passed exam will be reassessed by one or more summer assignments in advance of the supplemental session.

  Capping of reassessments applies to Theoretical Physics (TR035) students enrolled in this module. See full text at https://www.tcd.ie/teaching-learning/academic-affairs/ug-prog-award-regs/derogations/by-school.php  Select the year and scroll to the School of Physics.

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.