PH5460 Classical Field Theory

This is the homepage for the course PH5460 Classical Field Theory that I am teaching to students at IIT Madras during Fall 2014.

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Assessment

Assignments	25
Best of 2 Quizzes	25
Final	50
Total	100

Assignments

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

Notes and Handouts

A prelude to SR || Symplectic matrices have det=1 || Equivalences of Lie Algebras || | Finite-Energy Time-Independent Solutions and Derrick's Theorem ||

Interesting Links

The story behind the calculus of variations || Prof. Balakrishnan's Overview Lecture in his NPTEL lectures on Nonlinear Dynamics is a must see!|| Group Theory by J. S. Milne || Semi-Simple Lie Algebras and their Representations by Robert Cahn ||

For the patient student

• Gross' lectures on abstract algebra at Harvard gives a nice mathematical intro to group theory (and a lot more) and the text is one of my favourite books "Algebra" by M. Artin which I strongly recommend to all budding theoretical physicists.

Official Course Content

+ See 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

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