Finster, Felix and Kamran, Niky (2021) Complex structures on jet spaces and bosonic Fock space dynamics for causal variational principles. PURE AND APPLIED MATHEMATICS QUARTERLY, 17 (1). pp. 55-140. ISSN 1558-8599, 1558-8602
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Based on conservation laws for surface layer integrals for critical points of causal variational principles, it is shown how jet spaces can be endowed with an almost-complex structure. We analyze under which conditions the almost-complex structure can be integrated to a canonical complex structure. Combined with the scalar product expressed by a surface layer integral, we obtain a complex Hilbert space ( h, .vertical bar.). The Euler-Lagrange equations of the causal variational principle describe a nonlinear time evolution on h. Rewriting multilinear operators on h as linear operators on corresponding tensor products and using a conservation law for a nonlinear surface layer integral, we obtain a linear norm-preserving time evolution on bosonic Fock spaces. The so-called holomorphic approximation is introduced, in which the dynamics is described by a unitary time evolution on the bosonic Fock space. The error of this approximation is quantified. Our constructions explain why and under which assumptions critical points of causal variational principles give rise to a second-quantized, unitary dynamics on Fock spaces.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | causal variational principles; surface layer integrals; complex structures; bosonic Fock spaces; Hilbert space structures on jets |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Felix Finster |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 28 Jul 2022 09:39 |
| Last Modified: | 28 Jul 2022 09:39 |
| URI: | https://pred.uni-regensburg.de/id/eprint/46145 |
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