Trace class operators and states in p-adic quantum mechanics

• URL: http://arxiv.org/abs/2210.01566v2
• Date: Fri, 28 Oct 2022 09:01:03 GMT
• Title: Trace class operators and states in p-adic quantum mechanics
• Authors: Paolo Aniello, Stefano Mancini, Vincenzo Parisi
• Abstract summary: We show that one can define a suitable space of trace class operators in the non-Archimedean setting. The analogies, but also the several (highly non-trivial) differences, with respect to the case of standard quantum mechanics in a complex Hilbert space are analyzed.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Within the framework of quantum mechanics over a quadratic extension of the non-Archimedean field of p-adic numbers, we provide a definition of a quantum state relying on a general algebraic approach and on a p-adic model of probability theory. As in the standard complex case, a distinguished set of physical states are related to a notion of trace for a certain class of bounded operators and, in fact, we show that one can define a suitable space of trace class operators in the non-Archimedean setting, as well. The analogies, but also the several (highly non-trivial) differences, with respect to the case of standard quantum mechanics in a complex Hilbert space are analyzed.

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