相关论文: Quadratic tomography star product algebra and its …
Deforming the algebraic structure of geometric algebra on the phase space with a Moyal product leads naturally to supersymmetric quantum mechanics in the star product formalism.
The formalism of geometric algebra can be described as deformed super analysis. The deformation is done with a fermionic star product, that arises from deformation quantization of pseudoclassical mechanics. If one then extends the…
A review of the symplectic tomographic approaches within the framework of star-product quantization is presented. The classical statistical mechanics within the framework of the tomographic representation is considered. The kernels of…
A star-product formalism describing deformations of the standard quantum mechanical harmonic oscillator is introduced. A number of existing generalized oscillators occur as particular choises of star-products between the elements of the…
We study star product algebras of analytic functions for which the power series defining the products converge absolutely. Such algebras arise naturally in deformation quantization theory and in noncommutative quantum field theory. We…
A review of the photon-number tomography and symplectic tomography as examples of star-product quantization is presented. The classical statistical mechanics is considered within the framework of the tomographic representation.
Based on a closed formula for a star product of Wick type on $\CP^n$, which has been discovered in an earlier article of the authors, we explicitly construct a subalgebra of the formal star-algebra (with coefficients contained in the…
Given a star product with separation of variables $\star$ on a pseudo-K\"ahler manifold $M$ and a point $x_0 \in M$, we construct an associative algebra of formal distributions supported at $x_0$. We use this algebra to express the formal…
Quantization of classical systems using the star-product of symbols of observables is discussed. In the star-product scheme an analysis of dual structures is performed and a physical interpretation is proposed. At the Lie algebra level…
We study properties of a family of algebraic star products defined on coadjoint orbits of semisimple Lie groups. We connect this description with the point of view of differentiable deformations and geometric quantization.
We elaborate on the notion of generalized tomograms, both in the classical and quantum domains. We construct a scheme of star-products of thick tomographic symbols and obtain in explicit form the kernels of classical and quantum generalized…
The existing relation between the tomographic description of quantum states and the convolution algebra of certain discrete groupoids represented on Hilbert spaces will be discussed. The realizations of groupoid algebras based on qudit,…
Deformation quantization is a powerful tool for quantizing theories with bosonic and fermionic degrees of freedom. The star products involved generate the mathematical structures which have recently been used in attempts to analyze the…
We apply the star product quantization to the Lie algebra. The quantization in terms of the star product is well known and the commutation relation in this case is called the $\theta$-deformation where the constant $\theta$ appears as a…
The purpose of this Note is to unify quantum groups and star-products under a general umbrella: quantum groupoids. It is shown that a quantum groupoid naturally gives rise to a Lie bialgebroid as a classical limit. The converse question,…
This short summary of recent developments in quantum compact groups and star products is divided into 2 parts. In the first one we recast star products in a more abstract form as deformations and review its recent developments. The second…
The star product formalism has proved to be an alternative formulation for nonrelativistic quantum mechanics. We want introduce here a covariant star product in order to extend the star product formalism to relativistic quantum mechanics in…
We deform the group of Hamiltonian diffeomorphisms into the group of Hamiltonian automorphisms of a formal star product on a symplectic manifold. We study the geometry of that group and deform the Flux morphism in the framework of…
We present a deformation of the Minkowski space as embedded into the conformal space (in the formalism of twistors) based in the quantum versions of the corresponding kinematic groups. We compute explicitly the star product, whose Poisson…
A one parameter set of noncommutative complex algebras is given. These may be considered deformation quantisation algebras. The commutative limit of these algebras correspond to the algebra of polynomial functions over a manifold or…