2015/05/22 by Dirk-André Deckert, Deckert, D. -A., Franz Merkl +1 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.1505.06039
openalex publication_date 2015/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Shale-Stinespring Theorem (1965) together with Ruijsenaar's criterion (1977) provide a necessary and sufficient condition for the implementability of the evolution of external field quantum electrodynamics between constant-time hyperplanes on standard Fock space. The assertion states that an implementation is possible if and only if the spacial components of the external electromagnetic four-vector potential Aμ are zero. We generalize this result to smooth, space-like Cauchy surfaces and, for general Aμ, show how the second-quantized 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 Aμ w.r.t. the particular Cauchy surface, and show that they behave naturally under Lorentz and gauge transformations.