Unit 1

Continuum Mechanics: Review of Classical Mechanics: Lagrangian and Hamiltonian formalisms, Transformation theory, Action-Angle variables, Hamilton-Jacobi equations. Lagrangian and symmetries: Energy-Momentum tensor, Noether’s theorem and applications

Unit 2

Electromagnetism as a classical field theory: Lorentz transformation, The electromagnetic field tensor, covariant charge density and current, action formalism for electrodynamics, Maxwell’s equations and relativistic covariance, Lagrangian and Hamiltonian formalism, Symmetries and covariance, Gauge invariance.

Unit 3

Classical Field Theory of Gravitation: Principle of equivalence, curvilinear coordinates, metric, connection, curvature tensor, energy-momentum tensor, Einstein field equations and its Newtonian limit.

Prerequisites: Classical Mechanics & Special Theory of Relativity
Course Objectives
The course introduces the concepts and calculations involved in classical field theory. It extensively explains the classical field theories of Electromagnetism and Gravitation

1. L. D. Landau and E. M. Lifshitz, The Classical Theory of Fields, Pergamon Press, 4th Edition, 1980.
2. G. Giachetta, L. Mangiarotti and G. Sardanashvily, Advanced Classical Field Theory, World Scientific, 2009.
3. Florian Scheck, Classical FieldTheory, Springer, 2012.