Related papers: Non-commutativity in polar coordinates
The mathematical formalism commonly used in treating nonlocal highly singular interactions is revised. The notion of support cone is introduced which replaces that of support for nonlocalizable distributions. Such support cones are proven…
We survey noncommutative spacetimes with coordinates being enveloping algebras of Lie algebras. We also explain how to do differential geometry on noncommutative spaces that are obtained from commutative ones via a Moyal-product type…
In this paper, we establish an extension of a noncommutative Bennett inequality with a parameter $1\leq r\leq2$ and use it together with some noncommutative techniques to establish a Rosenthal inequality. We also present a noncommutative…
We describe basic concepts of noncommutative geometry and a general construction extending the familiar duality between ordinary spaces and commutative algebras to a duality between Quotient spaces and Noncommutative algebras. Basic tools…
Representations of the celebrated Heisenberg commutation relations in quantum mechanics and their exponentiated versions form the starting point for a number of basic constructions, both in mathematics and mathematical physics (geometric…
A possible method to investigate non-Hermitian Hamiltonians is suggested through finding a Hermitian operator $\eta_+$ and defining the annihilation and creation operators to be $\eta_+$-pseudo-Hermitian adjoint to each other. The operator…
In this thesis we analyze extensions of classical electromagnetic dualities to the noncommutative (NC) 3D and 4D space-times. It is known that the noncomutativity parameter theta becomes its Hodge dual *theta through the NC 4D…
This paper is a very brief and gentle introduction to non-commutative geometry geared primarily towards physicists and geometers. It starts with a brief historical description of the motivation for non-commutative geometry and then goes on…
The Newtonian Potential is computed exactly in a theory that is fundamentally Non Commutative in the space-time coordinates. When the dispersion for the distribution of the source is minimal (i.e. it is equal to the non commutative…
By using a framework where the object of noncommutativity $\theta^{\mu\nu}$ represents independent degrees of freedom, we study the symmetry properties of an extended $x+\theta$ space-time, given by the group $P$', which has the…
In this work, oriented for students with knowledge of basics of linear algebra, we demonstrate, how the use of polar decomposition allows one to understand metric properties of non-degenerate linear operators in $R^2$.
Noncommutative version of D-dimensional relativistic particle is proposed. We consider the particle interacting with the configuration space variable $\theta^{\mu\nu}(\tau)$ instead of the numerical matrix. The corresponding Poincare…
This is an overview of recent results aimed at developing a geometry of noncommutative tori with real multiplication, with the purpose of providing a parallel, for real quadratic fields, of the classical theory of elliptic curves with…
Group-theoretical analysis of arbitrary polarization devices is performed, based on the theory of the Lorentz group. In effective "non-relativistic" Mueller case, described by 3-dimensional orthogonal matrices, results of the one…
We investigate a set of functional equations defining a projection in the noncommutative 2-torus algebra $A_{\theta}$. The exact solutions of these provide various generalisations of the Powers-Rieffel projection. By identifying the…
We study the generalization of S-duality to non-commutative gauge theories. For rank one theories, we obtain the leading terms of the dual theory by Legendre transforming the Lagrangian of the non-commutative theory expressed in terms of a…
We discuss the polar in symbol space to hypoelliptic and partially hypoelliptic operators, assuming a transmission property related to a rectifiable boundary and using a representation based on two scalar products.
The noncommutativity concept has wide range of applications in physical and mathematical theories. Noncommutativity in the position-time coordinates concerns the microscale structure of space-time. the noncommutativity is an intrinsic…
Noncommutative phase space of an arbitrary dimension is considered. The both of operators coordinates and momenta in noncommutative phase space may be noncommutative. In this paper, we introduce momentum-momentum noncommutativity in…
It is well known that an (in general, non-commutative) set of non-Hermitian operators $\Lambda_j$ with real eigenvalues need not necessarily represent observables. We describe a specific class of quantum models in which these operators plus…