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Problems of Stability for Quantum Fields in External Time-Dependent Potentials
Phys. Rev. D 2, 2927 – Published 15 December, 1970
DOI: https://doi.org/10.1103/PhysRevD.2.2927
Abstract
We discuss the algebraic aspect of the time evolution for various types of fields interacting with external potentials. This is a pure -number problem for the classical wave equations. In the case of interaction, the equation for exhibits the well-known consistency troubles and the breakdown of causality studied by Velo and Zwanziger. Other equations, for example, a modified form of the Joos-Weinberg equations, are shown to lead to different troubles. As for the question of a unitary operator implementing the time-evolution automorphism in the Fock space of the in-fields, we encounter a peculiar property: The scalar coupling of fields (superrenormalizable) leads to the existence of a time-evolution operator, whereas electromagnetic-type couplings (renormalizable) possess at most an matrix and no evolution operator in the interaction region. This Haag's phenomenon holds for arbitrary smooth and short-range external fields.
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