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Classical Field Theory

Classical Field Theory. Instructor: Professor Suresh Govindarajan, Department of Physics, IIT Madras. The course introduces the student to relativistic classical field theory. The basic object is a field (such as the electromagnetic field) which possesses infinite degrees of freedom. The use of local and global symmetries (such as rotations) forms an underlying theme in the discussion.

Concepts such as conservation laws, spontaneous breakdown of symmetry, Higgs mechanism etc. are discussed in this context. Several interesting solutions to the Euler-Lagrange equations of motion such as kinks, vortices, monopoles and instantons are discussed along with their applications.

The Standard Model of particle physics is used to illustrate how the various concepts discussed in this course are combined in real applications. All necessary mathematical background is provided to make the course self-contained. This course may also be considered as a prelude to Quantum Field Theory. (from nptel.ac.in)

Lecture 19 - Lie Algebras I

Go to the Course Home or watch other lectures:

Lecture 01 - What is Classical Field Theory?

Lecture 02 - Symmetries and Invariances I

Lecture 03 - Symmetries and Invariances II

Lecture 04 - Group Theory in Physics I

Lecture 05 - Group Theory in Physics II

Lecture 06 - Finite Groups I

Lecture 07 - Finite Groups II

Lecture 08 - Basics of Classical Field Theory I

Lecture 09 - Basics of Classical Field Theory II

Lecture 10 - Basics of Classical Field Theory III

Lecture 11 - Green Functions I

Lecture 12 - Green Functions II

Lecture 13 - Noether's Theorem I

Lecture 14 - Noether's Theorem II

Lecture 15 - The Kink Soliton

Lecture 16 - Hidden Symmetry (Spontaneous Breakdown of Symmetry)

Lecture 17 - Local Symmetries

Lecture 18 - The Abelian Higgs Model

Lecture 19 - Lie Algebras I

Lecture 20 - Lie Algebras II

Lecture 21 - Magnetic Vortices I

Lecture 22 - Magnetic Vortices II

Lecture 23 - Non-abelian Gauge Theories I

Lecture 24 - Non-abelian Gauge Theories II

Lecture 25 - Irreps of Lie Algebras I

Lecture 26 - Irreps of Lie Algebras II

Lecture 27 - The Standard Model I

Lecture 28 - The Standard Model II

Lecture 29 - The Irreps of the Lorentz/Poincare Algebras

Lecture 30 - The Dirac Monopole

Lecture 31 - The 't Hooft-Polyakov Monopole

Lecture 32 - Revisiting Derrick's Theorem

Lecture 33 - The Julia-Zee Dyon

Lecture 34 - Instantons I

Lecture 35 - Instantons II

Lecture 36 - Instantons III

Lecture 37 - Instantons IV

Lecture 38 - Dualities

Lecture 39 - Geometrization of Field Theory