Related papers: Noncommutative Hypergeometry
In this review article we discuss some of the applications of noncommutative geometry in physics that are of recent interest, such as noncommutative many-body systems, noncommutative extension of Special Theory of Relativity kinematics,…
Several new identities for elliptic hypergeometric series are proved. Remarkably, some of these are elliptic analogues of identities for basic hypergeometric series that are balanced but not very-well-poised.
These notes aim to give an introduction to a few aspects of noncommutative geometry.
The aim of this note is to provide a new identity connected with the Gauss hypergeometric function. This is achieved using results of certain combinatorial identities and a hypergeometric function approach.
In this paper, we define a new type multivariable hypergeometric function. Then, we obtain some generating functions for these functions. Furthermore, we derive various families of multilinear and multilateral generating functions for these…
We reconsider differential geometry from the point of view of the quantum theory of non-relativistic spinning particles, which provides examples of supersymmetric quantum mechanics. This enables us to encode geometrical structure in…
This paper introduces arithmetic geometry for polynomial identity algebras using non-commutative (formal) deformation theory. Since formal deformation theory is inherently local the arithmetic and geometric results that follow give local…
In this work, generalized hypergeometric functions for bicomplex argument is introduced and its convergence criteria is derived. Furthermore, integral representation of this function has been established. Moreover, quadratic transformation,…
A construction of conservation laws for $\sigma$-models in two dimensions is generalized in the framework of noncommutative geometry of commutative algebras. This is done by replacing the ordinary calculus of differential forms with other…
We show how certain hypergeometric functions play an important role in finding fundamental solutions for a generalized Tricomi operator.
We briefly sketch the noncommutative geometry approach to the Standard Model, with attention to what can be inferred about particle masses.
We review basic notions and methods of noncommutative geometry and their applications to analysis and geometry on foliated manifolds.
We give a new proof that bounded non-commutative functions on polynomial polyhedra can be represented by a realization formula, a generalization of the transfer function realization formula for bounded analytic functions on the unit disk.
We aim to introduce a new extension of beta function and to study its important properties. Using this definition, we introduce and investigate new extended hypergeometric and confluent hypergeometric functions. Further, some hybrid…
A summary of noncommutative spectral geometry as an approach to unification is presented. The role of the doubling of the algebra, the seeds of quantization and some cosmological implications are briefly discussed.
Noncommutative geometry allows to unify the basic building blocks of particle physics, Yang-Mills-Higgs theory and General relativity, into a single geometrical framework. The resulting effective theory constrains the couplings of the…
We discuss non commutative functions, which naturally arise when dealing with functions of more than one matrix variable.
Holomorphic (nondegenerate) mappings between complex manifolds of the same dimension are of special interest. For example, they appear as coverings of complex manifolds. At the same time they have very strong "extra" extension properties in…
We begin by defining general hypergeometric functions over finite fields and obtaining a finite field analogue of a classical symmetry in their complex counterparts. We give a geometric proof for the symmetry by constructing isomorphisms…
This paper defines and examines the basic properties of noncommutative analogues of almost complex structures, integrable almost complex structures, holomorphic curvature, cohomology, and holomorphic sheaves. The starting point is a…