In the context of the field theory we show that for particles with opposite non-commutativity, in QED, there is no correction for the two-body bound state at the tree level. Consequently, the Helium atom is considered in the non-commutative space. It is shown that the effects of spatial non-commutativity appear at the tree level and they are of the order α. ∗ email: [email protected] † email...

We extend the non-commutative standard model based on the minimal SU(3)×SU(2)× U(1) gauge group to include the interaction of photon with neutrino. We show that, in the gauge invariant manner, only the right handed neutrino can directly couple to the photon. Consequently, we obtained the Feynman rule for the γνν̄-vertex which is not already existed in the minimal extension of non-commutative sta...

Non-commutative multi-variable versions of weighted shifts arise naturally as ‘weighted’ left creation operators acting on Fock space. We investigate the unital wot-closed algebras they generate. The unweighted case yields non-commutative analytic Toeplitz algebras. The commutant can be described in terms of weighted right creation operators when the weights satisfy a condition specific to the ...

In this paper, we arrive at the notion of equivalence classes of a non-commutative field exploring some ideas by Soloviev to nonlocal quantum fields. Specifically, an equivalence relation between non-commutative fields is formulated by replacing the weak relative locality condition by a weak relative asymptotic commutativity property, generalizing the notion of relative locality proved by Borch...

Let K be a (commutative) locally compact hypergroup with a left Haar measure. Let L1(K) be the hypergroup algebra of K and UCl(K) be the Banach space of bounded left uniformly continuous complex-valued functions on K. In this paper we show, among other things, that the topological (algebraic) center of the Banach algebra UCl(K)* is M(K), the measure algebra of K.

The aim of this notes is to provide basic information about commutative Banach algebras. The final goal is to show that a unital, commutative complex Banach algebra A can be embedded as subalgebra of C(MA), the algebra of continuous functions on a w∗-compact setMA, known as the maximal ideal space or character space. Also, the non unital commutative complex Banach algebra can be embedded as a s...

It is widely believed that the linearly realized BPS equation in the non-commutative space is related to the non-linearly realized BPS equation in the commutative space in the zero slope limit. We shall show that the relation also holds without taking the zero slope limit as is expected from arguments of the BPS equation for the non-Abelian Born-Infeld theory. This is regarded as an evidence fo...

By using the approach of non-commutative geometry, we study spinors and scalars on the two layers AdSd+1 space. We have found that in the boundary of two layers AdSd+1 space, by using the AdS/CFT correspondence, we have a logarithmic conformal field theory. This observation propose a way to get the quantum field theory in the context of non-commutative geometry. e-mail:kaviani,[email protected]...

A hypergroup is roughly speaking a locally compact Hausdorff space which has enough structure so that a convolution on the corresponding vector space of Radon measures makes it a Banach algebra. Hypergroups generalize in many ways topological groups. In this paper we extend to compact not necessarily commutative hypergroups some basic techniques on multipliers set forth for compact groups in He...

We construct exact vortex solutions to the equations of motion of the Abelian Higgs model defined in non commutative space, analyzing in detail the properties of these solutions beyond the BPS point. We show that our solutions behave as smooth deformations of vortices in ordinary space time except for parity symmetry breaking effects induced by the non commutative parameter θ. Associated with C...