We study the non-critical space-time non-commutative open string (NCOS) theory using a dual supergravity description in terms of a certain near-horizon limit of the F1-Dp bound state. We find the thermodynamics of NCOS theory from supergravity. The thermodynamics is equivalent to Yang-Mills theory on a commutative space-time. We argue that this fact does not have to be in contradiction with the...

We consider the Lorentz invariant non-commutative QED and complete the Feynman rules for the theory up to the order θ. In the Lorentz invariant version of the noncommutative QED the particles with fractional charges can be also considered. We show that in the parton model, even at the lowest order, the Bjorken scaling violates as ∼ θQ.

A non-commutative space X is a Grothendieck category ModX. We say X is integral if there is an indecomposable injective X-module EX such that its endomorphism ring is a division ring and every X-module is a subquotient of a direct sum of copies of EX . A noetherian scheme is integral in this sense if and only if it is integral in the usual sense. We show that several classes of non-commutative ...

The full algebra of relativistic quantum mechanics (Lorentz plus Heisenberg) is unstable. Stabilization by deformation leads to a new deformation parameter εl, l being a length and ε a ± sign. The implications of the deformed algebras for the uncertainty principle and the density of states are worked out and compared with the results of past analysis following from gravity and string theory. PA...

Matrix model is used as a regularization of field theory on non-commutative torus. However, there exists an example that the product of the large-N limit of matrices does not coincide with that of the corresponding fields. We propose a new procedure for regularizing fields on a non-commutative torus by matrices with the help of the projection in the representation space, so that the products of...

We present here a quite unexpected result: Apart from already known commutative C∗-algebras generated by Toeplitz operators on the unit ball, there are many other Banach algebras generated by Toeplitz operators which are commutative on each weighted Bergman space. These last algebras are non conjugated via biholomorphisms of the unit ball, non of them is a C∗-algebra, and for n = 1 all of them ...

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...

The noncommutative soliton is characterized by the use of the projection operators in non-commutative space. By using the close relation with the K-theory of C∗-algebra, we consider the variations of projection operators along the commutative directions and identify their topological charges. When applied to the string theory, it gives the modification of the brane charges due to tachyon backgr...

Bethe-Salpeter equation in the non-commutative space for a scalarscalar bound state is considered. It is shown that in the non-relativistic limit, the effect of spatial non-commutativity appears as if there exist a magnetic dipole moment coupled to each particle. e-mail: [email protected] e-mail: [email protected] Non-commutativity of space-time has been recently a subject of intense ...