This is the home page for the course, *PH546 Classical Field Theory*, that I am teaching during Fall 2008 (Aug.-Dec. 2008) at the Indian Institute of Technology Madras.

## Target Audience

It is an elective course in the M.Sc. as well as B.Tech. (Engg. Physics) curriculum. The class consists of M.Sc. students, B.Tech. (Engg. Physics) and students who are taking this course as a part of the Physics minor. I do have a few Ph.D. students as well.

## Assessment

- One Quiz — 25%
- Assignments — 25%
- Final Examination — 50%

## Course Notes

I plan to include notes (or links to notes by others) on various topics that are discussed in the class lectures.

**Elementary Group Theory:**Normal subgroups, Regular Representations,**Special Classical Solutions:**Solitons, Green Functions (to appear).**Lie Algebras and Lie Groups:**A note on (abstract) Lie Algebras (I show how the Jacobi identity follows from the associativity of group multiplication — this is usually not discussed in books! I don't prove the converse though.) Equivalences of Lie Algebras

## 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.

## References

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