Journal article
A discretization ofp-adic quantum mechanics
Communications in mathematical physics, Vol.135(2), pp.303-312
01/1991
DOI: 10.1007/BF02098045
Abstract
We show that some compact subgroups (ℋn,m) of the p-adic Heisenberg group act irreducibly on corresponding finite dimensional spaces of test-functions (Sm,n). Under certain conditions, a compact group (Am+n) of linear canonical transformations, isomorphic to SL(2, Zp), can be represented unitarily on Sm,n as a group of automorphisms of ℋn,m. The restriction to Sm,n can be considered as a discretization because an invariant subgroup (In,m) of Am+n is represented trivially. It is possible to take a limit where Im,n becomes an arbitrarily small neighborhood of the identity, while the dimension of Sm,n becomes arbitrarily large. This is a possible definition of the "continuum limit" that we relate to other projective limits appearing naturally in the present context. © 1991 Springer-Verlag.
Details
- Title: Subtitle
- A discretization ofp-adic quantum mechanics
- Creators
- Yannick Meurice - Centro de Investigación en Materiales Avanzados
- Resource Type
- Journal article
- Publication Details
- Communications in mathematical physics, Vol.135(2), pp.303-312
- DOI
- 10.1007/BF02098045
- ISSN
- 0010-3616
- eISSN
- 1432-0916
- Language
- English
- Date published
- 01/1991
- Academic Unit
- Physics and Astronomy
- Record Identifier
- 9984428665602771
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