Maxwell's equations

Maxwell's equations are the set of four equations, attributed to James Clerk Maxwell (written by Oliver Heaviside), that describe the behavior of both the electric and magnetic fields, as well as their interactions with matter.

Classical electrodynamics as a line bundle

An elegant and intuitive way to formulate Maxwell's equations is to use line bundles or principal bundles with fibre U(1). The connection on the line bundle is d+A with A the four-vector comprised of the electric potential and the magnetic vector potential. The curvature of the connection F=dA is the field strength. Some feel that this formulation allows a more natural description of the Aharonov-Bohm effect, namely in terms of the holonomy of a curve on a line bundle. (See Micheal Murray, Line Bundles, 2002 (PDF web link) for a simple mathematical review of this formulation. See also R. Bott, On some recent interactions between mathematics and physics, Canadian Mathematical Bulliten, 28 (1985) )no. 2 pp 129-164.)

Related Topics:
Line bundle - Principal bundle - U(1) - Connection - Four-vector - Electric potential - Magnetic vector potential - Curvature - Aharonov-Bohm effect

~ ~ ~ ~ ~ ~ ~ ~ ~ ~