Mathematical Physics Seminar, June 23, 2009
In the talk, I will present joint work with D. Deckert, D. Duerr, and M. Schottenloher on the time evolution of the second-quantized Dirac equation subject to a smooth and compactly supported, time-dependent electromagnetic field. Earlier work on this (e.g. Ruijsenaars) showed that the one-particle time evolution can be lifted to Fock space if and only if the external vector potential has zero magnetic potentials. The key idea (already observed by Fierz and Scharf) is to implement the time-evolution between varying Fock spaces. Representing varying Fock spaces as infinite wedge spaces gives a very intuitive, but rigorous picture. Our work on this subject was inspired by Dirac's original ideas, the work of Fierz and Scharf, Scharf's book, Pressley and Segal's book, and the work of Mickelsson. Preprint: arXiv:0906.0046 |