Memory effect in electromagnetic radiation

A memory effect is a net change in matter distribution due to radiation. It is a classically observable effect that takes place in the asymptotic region of spacetime. The study of memory effects started in gravitational physics where the effect is manifested as a permanent displacement in a configuration of test particles due to gravitational waves. Recently, analogous effects have been studied in the context of gauge theories. This thesis is focused on the memory effect present in electrodynamics. The study starts by a discussion on the fundamental aspects of electrodynamics as U(1) gauge invariant theory. Next, the tools of conformal compactification and Penrose diagram of Minkowski space are introduced. After these preliminaries, the electromagnetic analog of gravitational-wave memory, first analyzed by L. Bieri and D. Garfinkle, is studied in detail. Starting with Maxwell's equations, a partial differential equation is derived, in which the two-sphere divergence of the memory vector depends on the total charge flux F that reaches the null infinity and the initial and final values of the radial component of the electric field. The memory vector is then found to consist of two parts: the ordinary memory vector and the null memory vector. The solution of Bieri and Garfinkle for the null memory vector is reproduced by expanding the flux F in terms of spherical harmonics. Finally, the connection between the electromagnetic memory effect and the so-called asymptotic symmetries of U(1) gauge theory is analyzed. The memory effect is found to determine a large gauge transformation (LGT) in which the gauge parameter becomes a function of angles at null infinity. Since a LGT is a local symmetry of U(1) theory, there must be a conserved Noether current and Noether charge associated with it. As the memory effect generates a LGT, it is natural to expect a connection between the memory effect and the Noether charge. The study thus culminates in an equation that relates the conserved charge to the memory effect