Acausal quantum theory for non-Archimedean scalar fields
arXiv:1805.08613 · doi:10.1142/S0129055X19500119
Abstract
We construct a family of quantum scalar fields over a adic spacetime which satisfy adic analogues of the Gårding--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.
arXiv commentThird version, with some typos corrected. Accepted for publication in Reviews in Mathematical Physics (2019). Includes referee's suggestions
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