Entry requirements

120 credits with Mechanics III. Transform methods. Electromagnetic Field Theory.

Learning outcomes

On completion of the course the student shall be able to:

• interpret the deeper meaning of the Maxwellian field equations and account for their symmetry and transformation properties, domain of validity, and limitations
• formulate and solve electromagnetic problems with the help of electrodynamic potentials and superpotentials, and make a detailed account for gauge transformations and their use
• master the technique of deriving and evaluating formulae for the electromagnetic fields from very general charge and current distributions
• calculate the electromagnetic radiation from radiating systems (aerials, localised charge and current distributions) at rest
• calculate the electromagnetic radiation from localised charges which move arbitrarily in time and space, taking into account retardation effects. Account for the underlying approximations and assumptions
• formulate and solve electrodynamic problems in relativistically covariant form in four-dimensional space-time
• formulate self-consistent models for the interaction between matter and electromagnetic fields in relativistically covariant Lagrange and Hamilton formalism
• be familiar with some elementary phenomena and concepts in quantum electrodynamics

Content

Maxwell's equations. Energy and momentum formula in Maxwell's theory. Maxwell's stress tensor, radiation pressure. Telegraph equation. EM waves in vacuum and in media. Phase and group velocity, dispersion. The inhomogeneous wave equation. Gauge transformations, gauge invariance. Retarded potentials. Fields from random distributions of currents and charges. Super potentials. Electric and magnetic multipole radiation. Relativistic kinematics. Covariant formulation of electrodynamics. Liénard-Wiechert's potentials. Fields from a charged particle at random motion. Brehmsstrahlung, cyclotron and synchrotron radiation. Coherence and incoherence. Vavilov-Cerenkov radiation. Virtual photons. Radiation attenuation. Scattering from an individual charged particle. Absorption of radiation in an oscillator. Rayleigh scattering. Dispersion relations. Relativistic Lagrange and Hamilton formalism for charged particles in a field. Lagrange and Hamilton covariant equations for classical EM fields and interaction with charged particles. Periodic solutions in a box. Plane wave representation.

Instruction

Lectures, lessons and demonstration of computer simulations, project.

Assessment

Written examination at the end of the course. Project. Passed assignments may give bonus in the exam.