National University of Sciences and Technology
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PHY-920 Classical Field Theory
Campus SNS
Programs PG
Session Fall Semester 2016
Course Title Classical Field Theory
Course Code PHY-920
Credit Hours 3-0
Pre-Requisutes
Course Objectives Objectives: To introduce MPhil students to basic concepts of Field Theory

Outcomes: Students will understand,
  1. Special theory of Relativity
  2. Variational approach in physics
  3. Physics of continuous media
  4. Maxwell's equations
  5. theory of electromagnetic waves and radiation
Detail Content Development of pre-Newtonian and Newtonian mechanics. Need for Special Relativity (SR) and the Lorentz transformations for 1 and 3-d motion. Vector treatment of Lorentz transformations. Problems. Introduction to tensors. Four vector formulation of SR. Problems. Mass and energy in SR. Applications to Doppler and Compton effects, particle scattering, binding energy, particle production and decay. Problems. Functionals and functions. Differentiation of functionals relative to functions. The action integral and the objective functional. The calculus of variations. The brachistochrone problem. The Euler equation. Optimization. The Euler-Lagrange equations. The action for a point particle in SR and the EL equations. The general formulation of the Lagrangian for any field and the stress-energy-momentum tensor. The virial theorem. The laws of Coulomb, Gauss, Faraday, Ampere and Lorentz in 3-dimensional and 4-vector notation. The 4-vector potential and the Maxwell tensor; Maxwell’s equations, equation of continuity. Lagrangian and Hamiltonian formulations of electromagnetism. Gauge invariance. Motion in an electromagnetic field. Action functional of electromagnetic field. The electromagnetic field equations and stress-energy tensor. The energy density and energy flux. The virial theorem. The dipole and multipole moments. The multipole moment expansion of the static field. System of charges in an external field. Larmor’s theorem. Electromagnetic waves; plane waves; monochromatic plane waves; spectral resolution. Fourier resolution of the electrostatic field. Characteristic vibrations. Geometrical optics. Limits of geometrical optics. Fresnel and Fraunhoffer diffraction. Retarded potentials. Lienard-Wiechert potentials. Spectral resolution. The Lagrangian to second order. Field of system of charges at large distances. Electromagnetic radiation: multipole expansion; dipole and quadrupole radiation. The field at near distances. Synchrotron radiation. Radiation damping. Introduction to the Proca and Yang-Mills fields. Review of material.
Text/Ref Books Main Textbook: The Classical Theory of Fields
Author: L.D. Landau and E.M. Lifshitz (LL)
Publisher: Pergamon Press 1962

Textbooks: Relativity: An Introduction to the Special Theory
Author: Asghar Qadir (World Scientific, 1989)
Time Schedule Fall Semester 2014
Faculty/Resource Person Dr. Riwan Khalid
PhD, Physics (Delaware, USA)

Discipline: High Energy Physics