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Construction of \(p\)-adic covariant quantum fields in the framework of white noise analysis. (English) Zbl 1441.46055

Summary: In this article we construct a large class of interacting Euclidean quantum field theories, over a \(p\)-adic space time, by using white noise calculus. We introduce \(p\)-adic versions of the Kondratiev and Hida spaces in order to use the Wick calculus on the Kondratiev spaces. The quantum fields introduced here fulfill all the Osterwalder-Schrader axioms, except the reflection positivity.

MSC:

46S10 Functional analysis over fields other than \(\mathbb{R}\) or \(\mathbb{C}\) or the quaternions; non-Archimedean functional analysis
12H25 \(p\)-adic differential equations
60H40 White noise theory
81T05 Axiomatic quantum field theory; operator algebras
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