Course Details
Subject {L-T-P / C} : PH6118 : Classical Field Theory { 3-0-0 / 3}
Subject Nature : Theory
Coordinator : Dr. Bharat Kumar
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.
Course Objectives
- 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
Course Outcomes
On completion of the course, students will be able to: <br /> 1. demonstrates how to create a Lorentz invariant action in the context of scalar and vector fields. <br /> 2. learn about the scalar field theory, Maxwell field and Higg’s Mechanism. <br /> 3. learn about canonical quantization of the above-mentioned fields.
Essential Reading
- 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).
Supplementary Reading
- M. Carmeli, Classical Fields, Wiley (1982).
- A.O. Barut, Electrodynamics and Classical Theory of Fields, Chapter 1, MacMillan (1986).