The Bethe-Salpeter equation in non-commutative QED (NCQED) is considered for three-body bound state. We study the non-relativistic limit of this equation in the instantaneous approximation and derive the corresponding Schrödinger equation in non-commutative space. It is shown that the experimental data for Helium atom puts an upper bound on the magnitude of the parameter of non-commutativity, θ...

We describe a finite analogue of the Poisson Algebra of Wilson Loops in Yang–Mills theory. It is shown that this algebra arises in an apparently completely different context: as a Lie algebra of vector fields on a non–commutative space. This suggests that non–commutative geometry plays a fundamental role in the manifestly gauge invariant formulation of Yang–Mills theory. We also construct the d...

We consider field theory on non-commutative superspace and non-commutative spacetime that arises on D-branes in Type II superstring theory in constant self-dual graviphoton and NS-NS B field background. N = 1 supersymmetric field theories on this noncommutative space ( these theories are called N = 1/2 supersymmetric theory ) can be reduced to supermatrix models as in hep-th/0303210 [1]. We tak...

This paper concerns the closed points, closed subspaces, open subspaces, weakly closed and weakly open subspaces, and effective divisors, on a non-commutative space.

We introduce the notion of asymptotically almost nonexpansive curves which include almost-orbits of commutative semigroups of asymptotically nonexpansive type mappings and study the asymptotic behavior and prove nonlinear ergodic theorems for such curves. As applications of our main theorems, we obtain the results on the asymptotic behavior and ergodicity for a commutative semigroup of non-Lips...

We construct quantized free superfields and represent them as operator-valued distributions in Fock space starting with Majorana fields. The perturbative construction of the S-matrix for interacting theories is carried through by extending the causal method of Epstein and Glaser to superspace. We propose a scaling and singular order of distributions in superspace by a procedure which scales bot...

In the recent years, field theory on non-commutative (NC) spaces has attracted a lot of attention. Most literature on this subject deals with perturbation theory, although the latter runs into grave problems beyond one loop. Here we present results from a fully non-perturbative approach. In particular, we performed numerical simulations of the λφ model with two NC spatial coordinates, and a com...

The space-time symmetry of noncommutative quantum field theories with a deformed quantization is described by the twisted Poincaré algebra, while that of standard commutative quantum field theories is described by the Poincaré algebra. Based on the equivalence of the deformed theory with a commutative field theory, the correspondence between the twisted Poincaré symmetry of the deformed theory ...

This note is devoted to the study of geometric properties and the relationships between a projective space and an exponential class, both naturally associated with the positive elements in a commutative Banach algebra. Even though the motivating problem consists of understanding the geometry of the class of densities with respect to a given measure, the formulation can be carried out in general...

Let G be a complex algebraic group and L an algebraic subgroup of G. The quotient space G/L is called weakly commutative if a generic orbit of the action G : T ∗(G/L) is a coisotropic submanifold. We classify weakly commutative homogeneous spaces N L/L in the case where L is a reductive group and the natural representation L : n/[n, n], where n is the tangent algebra of the group N , is