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...

We propose a new higher-dimensional mechanism to localize scalar fields as well as fermionic and gauge fields. The underlying theory is a six-dimensional non-commutative field theory where non-commutativity is allowed along two extra infinite spatial dimensions and the four-dimensional brane is provided by a scalar soliton living in the non-commutative space. Making use of the powerful correspo...

The non-commutative geometry is revisited from the perspective of a generalized D p-brane. In particular, we analyze the open bosonic string world-sheet description and show that an effective non-commutative description on a D p-brane corresponds to a re-normalized worldvolume. The world-volume correlators are analyzed to make a note on the non-commutative geometry. It is argued that the U(1) g...

This paper contains detailed proofs of our results on the moduli space and the structure of noncommutative 3-spheres. We develop the notion of central quadratic form for quadratic algebras, and a general theory which creates a bridge between noncommutative differential geometry and its purely algebraic counterpart. It allows to construct a morphism from an involutive quadratic algebras to a C*-...

We introduce a smooth mapping of some discrete space-time symmetries into quasi-continuous ones. Such transformations are related with q-deformations of the dilations of the Euclidean space and with the non-commutative space. We work out two examples of Hamiltonian invariance under such symmetries. The Schrödinger equation for a free particle is investigated in such a non-commutative plane and ...

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...

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...

A definition is given and the physical meaning of quantum transformations of a non-commutative configuration space (quantum group coactions) is discussed. It is shown that non-commutative coordinates which are transformed by quantum groups are the natural generalization of the notion of a tensor operator for usual groups and that the quantum group coactions induce semigroups of transformations ...

We show that the moduli space of the (2, 0) and little-string theories compactified on T 3 with R-symmetry twists is equal to the moduli space of U(1) instantons on a noncommutative T . The moduli space of U(q) instantons on a non-commutative T 4 is obtained from little-string theories of NS5-branes at Aq−1 singularities with twists. A large class of gauge theories with N = 4 SUSY in 2+1D and N...