Classical Field Theory

This is the home page for the course, PH5460 (Classical Field Theory) that is being offered at IIT Madras during Fall 2012.


Assignments 25
One Quiz 25
Final 50
Total 100


There will be several graded assignments that will be handed out to the student.

Notes and Handouts

Normal Subgoups || Lie groups and Lie algebras || Symplectic matrices have det=1 || Equivalences of Lie Algebras || Milne's notes on Group Theory ||

Official Course Content

Lorentz transformations, infinitesimal generators, metric tensors, the light cone. Contravariant and covariant vectors.

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.

Complex scalar field: Lagrangian, field equations, global invariance.

Noether's theorem: transformations, rotations, Lorentz and gauge transformations as illustrations.

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

General covariance. Curved space, metric tensor, connection, parallel transport, covariant derivative, curvature tensor. Principle of equivalence. Gravitational field equations.


  1. L. D. Landau and E. M. Lifshitz, The Classical Theory of Fields, 4th edition, Pergamon (1975).
  2. M. R. Spiegel, Vector Analysis, Schaum Outline Series, McGraw-Hill (1974).
  3. M. Carmeli, Classical Fields, Wiley (1982).
  4. A. O. Barut, Electrodynamics and Classical Theory of Fields, Chap. 1, Macmillan (1986).
  5. C. Itzykson and J. B. Zuber, Quantum Field Theory, International Student Edition, Chap. 1, McGraw-Hill (1986).
  6. B. Schutz, A first course in General Relativity, Cambridge Univ. Press (1986).
  7. S. Coleman, Aspects of Symmetry, Cambridge Univ. Press.
  8. R. Rajaraman, Solitons and Instantons, North-Holland
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