Related papers: Induction of representations in deformation quanti…
The algebraic method of singular reduction is applied for non regular group action on manifolds which provides singular symplectic spaces. The problem of deformation quantization of the singular surfaces is the focus. For some examples of…
$C^*$-algebraic Weyl quantization is extended by allowing also degenerate pre-symplectic forms for the Weyl relations with infinitely many degrees of freedom, and by starting out from enlarged classical Poisson algebras. A powerful tool is…
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…
We give a quantum field theory interpretation of Kontsevich's deformation quantization formula for Poisson manifolds. We show that it is given by the perturbative expansion of the path integral of a simple topological bosonic open string…
We give a constructive approach for the study of integral representations of classical solutions to Poisson equations under some integrability conditions on data functions.
One way of reconciling classical and quantum mechanics is deformation quantization, which involves deforming the commutative algebra of functions on a Poisson manifold to a non-commutative, associative algebra, reminiscent of the space of…
Presented is a novel methodology for determining representational structure, which builds upon the existing Spotlight Resonance method. This new tool is used to gain insight into how discrete representations can emerge and organise in…
We demonstrate the relation between the isospectral deformation and Rieffel's deformation quantization by the action of $\mathbb{R}^d$.
This paper discusses the notion of a deformation quantization for an arbitrary polynomial Poisson algebra A. We examine the Hochschild cohomology group H^3(A) and find that if a deformation of A exists it can be given by bidifferential…
We consider the following construction of quantization. For a Riemannian manifold $M$ the space of forms on $T^*M$ is made into a space of (full) symbols of operators acting on forms on $M$. This gives rise to the composition of symbols,…
We place the renormalization procedure in quantum field theory into the familiar mathematical context of quantization of Poisson algebras. The Poisson algebra in question is the algebra of classical field theory Hamiltonians constructed in…
We investigate formal deformations of certain classes of nonassociative algebras including classes of K[{\Sigma}3]-associative algebras, Lie-admissible algebras and anti-associative algebras. In a process which is similar to Poisson algebra…
After a presentation of the context and a brief reminder of deformation quantization, we indicate how the introduction of natural topological vector space topologies on Hopf algebras associated with Poisson Lie groups, Lie bialgebras and…
Deformation quantization is a formal deformation of the algebra of smooth functions on some manifold. In the classical setting, the Poisson bracket serves as an initial conditions, while the associativity allows to proceed to higher orders.…
We present a short review of the approach to quantization known as strict (deformation) quantization, which can be seen as a generalization of the Weyl-Moyal quantization. We include examples and comments on the process of quantization.
We study when a finite dimensional Hopf action on a quantum formal deformation A of a commutative domain A_0 (i.e., a deformation quantization) must factor through a group algebra. In particular, we show that this occurs when the Poisson…
We will introduce formal frames of manifolds, which are a generalization of ordinary frames. Their fundamental properties are discussed. In particular, canonical forms are introduced, and torsions are defined in terms of them as a…
We canonically quantize a Poisson manifold to a Lie 2-groupoid, complete with a quantization map, and show that it relates geometric and deformation quantization: the perturbative expansion in $\hbar$ of the (formal) convolution of two…
Induced representations for quantum groups are defined starting from coisotropic quantum subgroups and their main properties are proved. When the coisotropic quantum subgroup has a suitably defined section such representations can be…
For a possibly singular subset of a regular Poisson manifold we construct a deformation quantization of its algebra of Whitney functions. We then extend the construction of a deformation quantization to the case where the underlying set is…