Representations of the Weyl group in spaces of square integrable functions with respect to \(p\)-adic valued Gaussian distributions. (English) Zbl 0903.46073

Albeverio, Sergio; Khrennikov, Andrei

J. Phys. A, Math. Gen. 29, No. 17, 5515-5527 (1996).

MSC:

46S10	Functional analysis over fields other than \(\mathbb{R}\) or \(\mathbb{C}\) or the quaternions; non-Archimedean functional analysis
81S05	Commutation relations and statistics as related to quantum mechanics (general)
46N50	Applications of functional analysis in quantum physics
47N50	Applications of operator theory in the physical sciences
81R05	Finite-dimensional groups and algebras motivated by physics and their representations

Keywords:

\(p\)-adic Hilbert space of functions; Weyl-Heisenberg group; operator quantization over \(p\)-adic numbers