Deckert, D.A.; Merkl, F.
(2016):
External Field QED on Cauchy Surfaces for Varying Electromagnetic Fields.
In: Communications in Mathematical Physics, Vol. 345, No. 3: pp. 9731017

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Abstract
The ShaleStinespring Theorem (J Math Mech 14:315322, 1965) together with Ruijsenaar's criterion (J Math Phys 18(4):720737, 1977) provide a necessary and sufficient condition for the implementability of the evolution of external field quantum electrodynamics between constanttime hyperplanes on standard Fock space. The assertion states that an implementation is possible if and only if the spatial components of the external electromagnetic fourvector potential are zero. We generalize this result to smooth, spacelike Cauchy surfaces and, for general , show how the secondquantized Dirac evolution can always be implemented as a map between varying Fock spaces. Furthermore, we give equivalence classes of polarizations, including an explicit representative, that give rise to those admissible Fock spaces. We prove that the polarization classes only depend on the tangential components of w.r.t. the particular Cauchy surface, and show that they behave naturally under Lorentz and gauge transformations.