Review of Classical Mechanics : Hamiltonians and Lagrangians. Legendre transforms and their properties. Euler-Lagrange equations. Principle of least action. (Functional calculus.) What is classical field theory – Vectors and Tensors : Group theory from invariances of classical equations – Newton’s equations and the Galilean group. Maxwell’s equations. Special Relativity and the Lorentz group. Vectors and tensors of the rotation and Lorentz groups. (Basics of group theory: definition, discrete groups and matrix groups.) – Basics of CFT : Systems with infinite degrees of freedom. Locality in space and time. Lagrangian densities for real and complex scalar fields. Euler-Lagrange (EL) equations. Functional calculus revisited. Hamiltonian density. The energy-momentum tensor – Solutions to the EL equations : Finite-energy time-independent solutions — classical vacua. Kinks in the Sine-Gordon and φ4 theories. Green functions as singular solutions. Boundary conditions.

Symmetries and Conservation Laws : Discrete and continuous symmetries. Noether’s theorem: the energy momentum tensor, the generalized angular momentum and the electromagnetic current. (Lie groups and Lie algebras. Representations of groups.) – The massless vector field : The Lagrangian density. Gauge invariance and the electromagnetic field strength. Maxwell’s equations. Lorentz invariants of the field strength. The symmetrized energy-momentum tensor. The generalized angular momentum and the spin of the photon – Secret Symmetry : Global symmetries. Spontaneous breakdown of symmetry. Goldstone’s theorem. (Coset spaces in group theory.) – Solitons : Solitons as finite-energy solutions. Derrick’s theorem. Getting around Derrick’s theorem. Local symmetries and gauge fields. Abelian vortices. The Dirac monopole as a singular solution of Maxwell’s equations. Dirac quantization – Local Symmetries : Abelian gauge fields. Covariant derivatives and minimal coupling. The abelian Higgs model. Vortex solutions (in type II superconductors). Topological conservation laws. The abelian Higgs mechanism.

Non-abelian gauge theories : Covariant derivatives; The Yang–Mills field strength; Coupling matter to non-abelian gauge fields; Higgs mechanism – SU(2)->U(1) and SO(3)->U(1) ; Weinberg’s theorem. The ‘t Hooft-Polyakov monopole as a non-singular solution. Julia-Zee dyons; the Bogomolnyi-Prasad- Sommerfield(BPS) limit. Dirac quantization for dyons – The Standard Model of Particle Physics as a CFT : Basic forces in nature. Symmetry breaking in the electroweak sector. Quantum Chromodynamics and the quark model – Instantons : Instantons as finite action solutions to the EL equations.The ‘t Hooft solution. Nahm and Bogomolnyi equations from dimensional reduction.

Other Resources

Course Curriculum

This course is part of NPTEL online courses, delivered by IIT Madras.

Course Reviews


  • 5 stars0
  • 4 stars0
  • 3 stars0
  • 2 stars0
  • 1 stars0

No Reviews found for this course.


FreeVideoLectures Provides you complete information about best courses online, Video tutorials, helps you in building a career !!

Learn More About us

About Us
Privacy Policy

top All rights reserved.

Setup Menus in Admin Panel