We consider static U(1) monopole in non-commutative space. Up to the second order in the non-commutativity scale θ, we find no non-trivial corrections to the Dirac solution, the monopole mass remains infinite. We argue the same holds for any arbitrary higher order. Some speculation about the nature of non-commutative spacetime and its relation to the cosmological constant is made. Non-commutati...

Extending earlier work [7], we examine the deformation of the canonical symplectic structure in a cotangent bundle T ⋆ (Q) by additional terms implying the Poisson non-commutativity of both configuration and momentum variables. In this short note, we claim this can be done consistently when Q is a Lie group.

A non–commutative analogue of the classical differential forms is constructed on the phase–space of an arbitrary quantum system. The non– commutative forms are universal and are related to the quantum mechanical dynamics in the same way as the classical forms are related to classical dynamics. They are constructed by applying the Weyl–Wigner symbol map to the differential envelope of the linear...

We treat the events determined by a quantum physical state in a non-commutative space-time, generalizing the analogous treatment in the usual Minkowski space-time based on positive-operator-valued measures (POVMs). We consider in detail the model proposed by Sny-der in 1947 and we calculate the POVMs defined on the real line that describe the measurement of a single coordinate. The approximate ...

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...

‎‎let r be a non-commutative ring with unity‎. ‎the commuting graph‎ ‎of $r$ denoted by $gamma(r)$‎, ‎is a graph with a vertex set‎ ‎$rsetminus z(r)$ and two vertices $a$ and $b$ are adjacent if and only if‎ ‎$ab=ba$‎. ‎in this paper‎, ‎we investigate non-commutative rings with unity of order $p^n$ where $p$ is prime and $n in lbrace 4,5 rbrace$‎. it is shown that‎, ‎$gamma(r)$ is the disjoint ...