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arXiv · 1805.08613

Acausal quantum theory for non-Archimedean scalar fields

M. L. Mendoza-Martínez·J. A. Vallejo·W. A. Zúñiga-Galindo
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Abstract

We construct a family of quantum scalar fields over a $p-$adic spacetime which satisfy $p-$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 $p-$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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M. L. Mendoza-Martínez, J. A. Vallejo, W. A. Zúñiga-Galindo. 2018-11-02. Acausal quantum theory for non-Archimedean scalar fields. https://doi.org/10.1142/s0129055x19500119

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