Ullrich, Peter (2004) On the restriction of quantum fields to a lightlike surface. JOURNAL OF MATHEMATICAL PHYSICS, 45 (8). pp. 3109-3145. ISSN 0022-2488,
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To treat the front-form Hamiltonian approach to quantum field theory, called light cone quantum field theory, in a mathematically rigorous way, the existence of a well-defined restriction of the corresponding free fields to the hypersurface {x(0)+x(3)=0} in Minkowski space is of an essential necessity. However, even in the situation of a real scalar free field such a restriction does canonically not exist; this is called the restriction problem. Furthermore, since the beginning of light cone quantum field theory there is the problem of nonexistence of a well-defined Fock space expansion of a free quantum field in terms of light cone momenta which is called the zero-mode problem. In this paper we present solutions to these long outstanding problems where the study of the zero-mode problem (of the corresponding classical field) will lead us to a solution of the restriction problem. We introduce a new function space of "squeezed" smooth functions which can canonically be embedded into the Schwartz space S(R-3). The restriction of the free field to {x(0)+x(3)=0} is canonically definable on this function space and we show that the covariant field is uniquely determined by this "tame" restriction. (C) 2004 American Institute of Physics.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | NULL PLANES; ALGEBRAS; FRONT; |
| Subjects: | 500 Science > 530 Physics |
| Divisions: | Physics > Institute of Theroretical Physics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 05 Jul 2021 12:32 |
| Last Modified: | 05 Jul 2021 12:32 |
| URI: | https://pred.uni-regensburg.de/id/eprint/37403 |
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