Acausal quantum theory for non-Archimedean scalar fields
High Energy Physics - Theory
2019-04-24 v3 Mathematical Physics
Functional Analysis
math.MP
Abstract
We construct a family of quantum scalar fields over a adic spacetime which satisfy adic analogues of the G\aa rding--Wightman axioms. Most of the axioms can be formulated the same way in both, the Archimedean and non-Archimedean frameworks; however, the axioms depending on the ordering of the background field must be reformulated, reflecting the acausality of adic spacetime. The adic scalar fields satisfy certain adic Klein-Gordon pseudo-differential equations. The second quantization of the solutions of these Klein-Gordon equations corresponds exactly to the scalar fields introduced here.
Cite
@article{arxiv.1805.08613,
title = {Acausal quantum theory for non-Archimedean scalar fields},
author = {M. L. Mendoza-Martínez and J. A. Vallejo and W. A. Zúñiga-Galindo},
journal= {arXiv preprint arXiv:1805.08613},
year = {2019}
}
Comments
Third version, with some typos corrected. Accepted for publication in Reviews in Mathematical Physics (2019). Includes referee's suggestions