منابع مشابه
Exponential Representations of the Canonical Commutation Relations
A class of representations of the canonical commutation relations is investigated. These representations, which are called exponential representations, are given by explicit formulas. Exponential representations are thus comparable to tensor product representations in the sense that they provide the possibility of computing useful criteria concerning various properties. In particular, they are ...
متن کاملC-Multipliers, crossed product algebras, and canonical commutation relations
The notion of a multiplier of a group X is generalized to that of a C-multiplier by allowing it to have values in an arbitrary C-algebra A. On the other hand, the notion of the action of X in A is generalized to that of a projective action of X as linear transformations of the space of continuous functions with compact support in X and with values in A. It is shown that there exists a one-to-on...
متن کاملExact Discrete Analogs of Canonical Commutation and Uncertainty Relations
An exact discretization of the canonical commutation and corresponding uncertainty relations are suggested. We prove that the canonical commutation relations of discrete quantum mechanics, which is based on standard finite difference, holds for constant wave functions only. In this paper, we use the recently proposed exact discretization of derivatives, which is based on differences that are re...
متن کاملUNIQUE MIXING OF THE SHIFT ON THE C–ALGEBRAS GENERATED BY THE q–CANONICAL COMMUTATION RELATIONS
aia + j − qa + j ai = δij1, i, j ∈ Z where −1 ≤ q ≤ 1. This gives an interpolation between the canonical commutation relations (Bosons) when q = 1 and the canonical anticommutation relations (Fermions) when q = −1, while when q = 0 we have freeness (cf. [16]). In [3], (see also [9] and [7]) a Fock representation of these relations was found, giving annihilators ai and their adjoints, the creato...
متن کاملThe semantics of the canonical commutation relation
1.1 This paper is a part of a much broader project which aims to establish, for a typical ’co-ordinate algebra’ A in the sense of non-commutative geometry, or a scheme, a geometric counterpart VA. Here “geometric” should also be understood in some broad but well-defined sense. We believe this is possible in the setting of model theory, where a crucial new experience in generalisation of semanti...
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ژورنال
عنوان ژورنال: MATHEMATICA SCANDINAVICA
سال: 1973
ISSN: 1903-1807,0025-5521
DOI: 10.7146/math.scand.a-11448