The Dirac evolution equation in the presence of an electromagnetic wave

Radu Purice, Anne Boutet De Monvel-Berthier
We consider the Diiac evolution equation in presence of a time dependent electromagnetic potential which is a solution of the homogenous wave equation with tegular and compactly supported initial data. We prove a propagation property for the free Dirac Hamiltonian using the explicit form of the free propagator that we use together with an energy estimation and the finite propagation speed of the Dirac evolution we prove existence and unitarity of the wave operators associated to the couple of
more » ... rac evolutions: the free one and the time dependent one.
doi:10.5169/seals-116645 fatcat:6x4qgjnejrfrjexb5nu54l76qa