Commutative H *-algebra is characterized in terms of idempotents. Here we offer three characterizations. 1. Introduction. In the past, the author used commuting idempotents to characterize continuous functions defined on a certain space [3, 4]. For example , it was shown in [3] that a certain Banach algebra is isometrically isomorphic to the space C(S) of all continuous complex-valued functions...

We construct an exact regular vortex solution to the self-dual equations of the Abelian Higgs model in non-commutative space for arbitrary values of θ. To this end, we propose an ansatz which is the analogous, in Fock space, to the one leading to exact solutions for the Nielsen-Olesen vortex in commutative space. We compute the flux and energy of the solution and discuss its relevant properties.

The groupoid approach to noncommutative unification of general relativity with quantum mechanics is compared with the canonical gravity quantization. It is shown that by restricting the corresponding noncommutative algebra to its (commutative) subalgebra, which determines the space-time slicing, an algebraic counterpart of superspace (space of 3-metrics) can be obtained. It turns out that when ...

This paper considers the effects of space noncommutativity on the thermodynamics of a Reissner-Nordström black hole. In the first step, we extend the ordinary formalism of Bekenstein-Hawking to the case of charged black holes in commutative space. In the second step we investigate the effects of space noncommutativity and the generalized uncertainty principle on the thermodynamics of charged bl...

In this work, we present a gauge principle that starts with the momentum space representation of position operator (x^i=iℏ∂∂pi), rather than starting (p^i=−iℏ∂∂xi). This extension can be seen as dynamical version Born’s reciprocity theory, which exchanges and momentum. We discuss some simple examples new type theory: (i) analog solutions from ordinary theory in (ii) Landau levels using fields, ...