Sergio Albeverio and Andrew Khrennikov 1996 J. Phys. A: Math. Gen. 29 5515 doi:10.1088/0305-4470/29/17/023
Representations of the Weyl group in spaces of square integrable functions with respect to p-adic valued Gaussian distributions
Sergio Albeverio and Andrew Khrennikov
Show affiliationsWe construct a representation of the Weyl group in the p-adic Hilbert space of functions which are square integrable with respect to a p-adic valued Gaussian distribution. The operators corresponding to position and momentum are determined by groups of unitary operators with parameters restricted to some balls in the field 
of p-adic numbers. A surprising fact is that the radii of these balls are connected by `an uncertainty relation' which can be considered as a p-adic analogue of the Heisenberg uncertainty relations. The p-adic Hilbert space representation of the Weyl group is the basis for a calculus of pseudo-differential operators and for an operator quantization over p-adic numbers.
- PACS
- MSC
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47L30 Abstract operator algebras on Hilbert spaces
81R12 Relations with integrable systems (See also 17Bxx, 37J35)
- Subjects
- Dates
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Issue 17 (7 September 1996)
Received 26 October 1995, in final form 18 March 1996
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Representations of the Weyl group in spaces of square integrable functions with respect to p-adic valued Gaussian distributions
Sergio Albeverio and Andrew Khrennikov 1996 J. Phys. A: Math. Gen. 29 5515
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