Syllabus

Lorentz transformations: infinitesimal generators, metric tensors, the light cone. Contravariant and covariant vectors and tensors. Classical field theory of a real scalar field: action, Lagrangian density, Euler-Lagrange field equation. The conjugate momentum. Hamiltonian density, energy-momentum tensor, physical interpretation. Angular momentum tensor for a real scalar field. Invariance under Lorentz transformations and conservation of angular momentum. Internal degrees of freedom and symmetrization of the energy-momentum tensor.
complex scalar field: Lagrangian, field equations, global field invarience.
Noether's theorem: transformations, invariance and conserved quantities. Translations, rotations, Lorentz and gauge transformations as illustrations.

The massless vector field: Lagrangian, field equations, Lorentz condition. The field tensor, Maxwell's equations. Energy density, Poynting vector. Invariance of the electromagnetic field. Lorentz transformation properties of electric and magnetic fields. Minimal coupling of matter fields
to the electromagnetic field. Covariant derivative, local gauge invariance, continuity equation for the current, charge conservation.

Understand the Lagrange densities for a number of field theories

Know how to derive the equations of motion for these

Easy to switch between relativistic and non-relativistic formulations

On completion of the course, students will be able to:
1. demonstrates how to create a Lorentz invariant action in the context of scalar and vector fields.
2. learn about the scalar field theory, Maxwell field and Higg’s Mechanism.
3. learn about canonical quantization of the above-mentioned fields.

L.D. Landau and E.M. Lifshitz, The Classical Theory of Fields, 4th Edition, Pergamon (1975).

Ashok Das, Lectures on Quantum Field Theory, World Scientific Publishing Co. Pte. Ltd. (2008).

M. Carmeli, Classical Fields, Wiley (1982).

A.O. Barut, Electrodynamics and Classical Theory of Fields, Chapter 1, MacMillan (1986).