# Course Contents:

EM 2004

## 1. Relativity and field theories

Module duration: 4.5 hours

The symmetry properties of Maxwell's equations yield relativity. It will be shown how this formulation can be used to write down and analyse Maxwell's equations. In addition, we will briefly study theories of scalar fields, and of fields with internal symmetries.

Previous exposure to relativity will be assumed. In this part of the course I will mainly concentrate on the mathematical techniques needed to use relativity in the remainder of the course. The notion of symmetry groups will be introduced. Scalars, vectors, spinors and tensors will be defined through their transformation properties, and techniques for handling them will be introduced.

The material in the BaBaR teaching package is a prerequisite: check that you understand it. If you don't, then urgently read any of the books on special relativity in the library.

The text books by Jackson [1], Landau and Lifschitz [2] and Barut [4] are recommended for this part of the course. For motion faster than the speed of light (super-luminal motion) see R. Ehrlich, Am. J. Phys., 71 (2003) 1109 (Section II) and a neat demonstration in Greg Egan's applet. For the current status of experiments on super-luminal motion see the original articles.

## 2. The physics of mobile phones

Module duration: 10.5 hours

The Maxwell's equations will be written in terms of gauge potentials (scalar and vector potentials) in some selected gauges, the Green's functions will be constructed, and the retarded (Lienard-Weichert) potentials and fields obtained. We shall investigate the far-field behaviour of these fields and show that they involve propagation of electromagentic radiation. We will study the power output of antennae, and construct algorithms to locate people by their mobile phones.

Radiation from accelerated charges will be studied in greater detail. The spectral properties of the radiation will be extracted using the Green's functions. The physics of linear accelerators will be investigated. The spectral and polarisation properties of synchrotron radiation will be studied.

The mathematical methods to be used include the algebra of vectors and vector analysis including Gauss' and Stoke's theorems, as well as Fourier and spherical harmonic expansions. Knowledge of these topics at the Master's level are pre-requisites for the course. Tensors will be introduced.

Jackson [1] and Schwinger [3] are the main textbooks to use for this section. The web contains useful material on the wave equation and Maxwell's equations. For a beautiful explanation of the physical meaning of gauge invariance, see the article A. Shapere and F. Wilczek, "Gauge kinematics of deformable bodies", Am. J. Phys., 57 (1989) 514. Read this newspaper article on antennas and check whether you understand the physics of all the details given in the article. The Stanford Linear Accelerator Center (SLAC) has background information on particle accelerators. A Google search on accelerators gives interesting results. Read about Radar and its history in WWII. Check out the generation and uses of synchrotron radiation.

## 3. Magnetic monopoles and duality

Module duration: 1.5 hours

We will study some of the physical effects due to magnetic monopoles. In particular, we shall study a duality of the Maxwell's equations, and a peculiar behaviour of the vector potential.

The main textbooks for this section are Jackson [1] and Schwinger [3]. One of the best sources for this material is the first section of the article by P. Godard and D. Olive, "Magnetic monopoles in gauge field theories", Rep. Prog. Phys. 41 (1978) 1357, which is cached here (5236 Kb). The relativistic notation used in parts of the article are explained in the textbook by Landau and Lifschitz [2]. See also the lecture S. Coleman, "The magnetic monopole fifty years later", in The unity of fundamental interactions (ed. A. Zichichi) Plenum, New York, 1983, 21. The geometrical meaning of gauge freedom is explained in the article by M. Daniel and C.M. Viallet, "The geometrical setting of gauge theories of the Yang-Mills type", Rev. Mod. Phys., 52 (1980) 175, which is cached here (3982 kB).

## 5. Holding a BE condensate: ion traps

Module duration: 4.5 hours

The motion of charges in external electric and magnetic fields will be investigated. The notion of adiabatic invariants will be used to find qualitative features of motion in non-constant fields. Motion of charges in the earth's magnetic field will the studied. Various kinds of ion-traps will be examined.

Refer to Jackson [1] or Schwinger [3] and Sturrock [6] for this material. See an article on plasmas, and another on ion-traps and laser cooling.

## 6. Electromagnetic fields in matter

Module duration: 9 hours

Electromagnetic phenomena will be analysed in the presence of matter. The dielectric susceptibility and permittivity, the conductivity and related quantities will be introduced and used to study phenomena such as the Hall effect and piezoelectricity. Electrodynamics in superconductors will be considered briefly. Electromagnetic waves in cold plasmas will be studied and Debye screening and Landau damping will be discussed. Elementary analysis of the magnetohydrodynamic equations will be performed.

Use Landau, Lifschitz and Pitaevskii [5], Schwinger [3], Jackson [1] or Sturrock [6] for this part of the course. The textbooks may be needed to make sense of some of the material in the plasma science and technology pages. For fun, see an article on ferrofluids

© Sourendu Gupta. Created on Nov 05, 2003. Last updated on Nov 05, 2003.