Related papers: Deformation Quantization: Observable Algebras, Sta…

The algebra of diffeomorphisms derived from general coordinate transformations on commuting coordinates is represented by differential operators on noncommutative spaces. The algebra remains unchanged, the comultiplication however is…

We review the recent development in the representation theory of the $W_{1+\infty}$ algebra. The topics that we concern are, Quasifinite representation, Free field realizations, (Super) Matrix Generalization, Structure of subalgebras such…

In the context of deformation quantization, there exist various procedures to deal with the quantization of a reduced space M_red. We shall be concerned here mainly with the classical Marsden-Weinstein reduction, assuming that we have a…

We review deformed quantum phase spaces and their realizations in terms of undeformed phase space. In particular, methods of calculation for the star product, coproduct of momenta and twist from realizations are presented, as well as their…

We derive algebraic recurrence relations to obtain a deformation quantization with separation of variables for a locally symmetric K\"ahler manifold. This quantization method is one of the ways to perform a deformation quantization of…

Quantisation on spaces with properties of curvature, multiple connectedness and non orientablility is obtained. The geodesic length spectrum for the Laplacian operator is extended to solve the Schroedinger operator. Homotopy fundamental…

We study a Lie algebra type $\kappa$-deformed space with undeformed rotation algebra and commutative vector-like Dirac derivatives in a covariant way. Space deformation depends on an arbitrary vector. Infinitely many covariant realizations…

The subject of this thesis is the rigorous construction of QFT models with nontrivial interaction. Two different approaches in the framework of AQFT are discussed. On the one hand, an inverse scattering problem is considered. A given…

Let $\{{\cdot},{\cdot}\}_{\boldsymbol{\mathcal{P}}}$ be a variational Poisson bracket in a field model on an affine bundle $\pi$ over an affine base manifold $M^m$. Denote by $\times$ the commutative associative multiplication in the…

In this paper a new approach to investigation of Quantum and Statistical Mechanics of the Early Universe (Planck scale) - density matrix deformation - is proposed. The deformation is understood as an extension of a particular theory by…

In this article we study the quantization of a free real scalar field on a class of noncommutative manifolds, obtained via formal deformation quantization using triangular Drinfel'd twists. We construct deformed quadratic action functionals…

This work is the final version of my master thesis. Many, but not all of its key results are already available as a preprint with Chiara Esposito and Stefan Waldmann on arxiv.org under the title "Convergence of the Gutt Star Product", which…

A new deformed canonical commutation relation, generalizing various known deformations, is defined together with its structure function of deformation. Then, the related irreducible representations are characterized and classified. Finally,…

A quantization of classical deformation theory, based on the Maurer-Cartan Equation $dS + \frac{1}{2}[S,S] = 0$ in dg-Lie algebras, a theory based on the Quantum Master Equation $dS + \hbar \Delta S + \frac{1}{2} \{S,S\} = 0$ in…

We start from Rieffel data (A,f,X) where A is a C*-algebra, X is an action of an abelian group H on A and f is a 2-cocycle on the dual group. Using Landstad theory of crossed product we get a deformed C*-algebra A(f). In the case of H being…

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.

We provide and discuss complex analytic methods for overcoming the formal character of formal deformation quantization. This is a necessity for returning to physically meaningful statements, and accounts for the fact that the formal…

This is the text of the lecture given by the author in Naples at "Giornata IndAM", June 7, 2005. The lecture is addressed at the general mathematical audience and reviews several topics in deformation theory of associative algebras.

In his celebrated paper Kontsevich has proved a theorem which manifestly gives a quantum product (deformation quantization formula) and states that changing coordinates leads to gauge equivalent star products. To illuminate his procedure,…

This article is a survey of recent work of the authors developing a new approach to quantization based on the equivariance with respect to some Lie group of symmetries. Examples are provided by conformal and projective differential…