Acausal quantum theory for non-Archimedean scalar fields
Abstract
We construct a family of quantum scalar fields over a p-adic spacetime which satisfy p-adic analogues of the G 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 p-adic spacetime. The p-adic scalar fields satisfy certain p-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.
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