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- Albeverio, Sergio, et al.
(författare)
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p-Adic valued quantization
- 2009
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Ingår i: P-Adic Numbers, Ultrametric Analysis, and Applications. - Berlin : Springer. - 2070-0466 .- 2070-0474. ; 1:2, s. 91-104
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Forskningsöversikt (refereegranskat)abstract
- This review covers an important domain of p-adic mathematical physics — quantum mechanics with p-adic valued wave functions. We start with basic mathematical constructions of this quantum model: Hilbert spaces over quadratic extensions of the field of p-adic numbers ℚ p , operators — symmetric, unitary, isometric, one-parameter groups of unitary isometric operators, the p-adic version of Schrödinger’s quantization, representation of canonical commutation relations in Heisenberg andWeyl forms, spectral properties of the operator of p-adic coordinate.We also present postulates of p-adic valued quantization. Here observables as well as probabilities take values in ℚ p . A physical interpretation of p-adic quantities is provided through approximation by rational numbers.
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