Related papers: Commutation Formulae With Respect to Non-Symmetric…
Any flat connection on a principal fibre bundle comes from a linear representation of the fundamental group. The noncommutative analog of this fact is discussed here.
The non-associativity of translations in a quantum system with magnetic field background has received renewed interest in association with topologically trivial gerbes over $\mathbb{R}^n.$ The non-associativity is described by a 3-cocycle…
We review some applications of noncommutative geometry to the study of transverse geometry of Riemannian foliations and discuss open problems.
There exists two types of nonassociative algebras whose associator satisfies a symmetric relation associated with a 1-dimensional invariant vector space with respect to the natural action of the symmetric group on three elements. The first…
This paper presents a method for constructing flat deformations of associative algebras. We will refer to this method as method two because it is a generalisation of the method obtained in [1]. The deformations obtained using the first two…
We give the generalization of a recent variational formulation for nonconservative classical mechanics, for fermionic and sypersymmetric systems. Both cases require slightly modified boundary conditions. The supersymmetric version is given…
The central theme of this thesis is noncommutativity in string theory. We explore in detail how noncommutative structures can emerge in case of the interacting bosonic string and even in the fermionic sector of superstring theory. We have…
4x4x3 absolutely nonsingular tensors are characterized by their determinant polynomial. Non-quivalence among absolutely nonsingular tensors with respect to a class of linear transformations, which do not chage the tensor rank,is studied. It…
We establish several summation formulae for hypergeometric and basic hypergeometric series involving noncommutative parameters and argument. These results were inspired by a recent paper of J. A. Tirao [Proc. Nat. Acad. Sci. 100 (14)…
A new functional model for pairs of commuting isometries is described. Intertwining operators between such models are then studied in order to approach the classification of invariant subspaces of such pairs.
Operator nucleon vertices are constructed in composite superconformal string model. Splitting of baryon Regge trajectories with the same quantum numbers but with opposite parity is provided by inclusion of simple additional components to…
A non-commutative formula for the isotropic magneto-electric response of disordered insulators under magnetic fields is derived using the methods of non-commutative geometry. Our result follows from an explicit evaluation of the Ito…
A novel approach to the analysis of a noncommutative Chern--Simons gauge theory with matter coupled in the adjoint representation has been discussed. The analysis is based on a recently proposed closed form Seiberg--Witten map which is…
This paper presents an overview of physical ideas and mathematical methods for implementing non-smooth and discontinuous substitutions in dynamical systems. General purpose of such substitutions is to bring the differential equations of…
The appearance of noncommuting spatial coordinates is studied in quantum systems containing a magnetic monopole and under the influence of a radial potential. We derive expressions for the commutators of the coordinates that have been…
We consider the problem of decomposing a real-valued symmetric tensor as the sum of outer products of real-valued vectors. Algebraic methods exist for computing complex-valued decompositions of symmetric tensors, but here we focus on…
It is always stated that the position operator for massless particles has non-comutting components. It is shown that the reason is that the commutation relations between coordinates and momenta differs for massive and massless particles.…
In this paper we derive a formula for a covariance matrix of any self-affine measure.
Recently, spin splitting of non-relativistic origin in compensated antiferromagnets has drawn growing attention in condensed matter research. Although many materials, now known to exhibit such spin splitting, have been studied for decades,…
We define and study the theory of derivation-based connections on a recently introduced class of bimodules over an algebra which reduces to the category of modules whenever the algebra is commutative. This theory contains, in particular, a…