相关论文: Deformation quantization on a Hilbert space
Starting with the well-defined product of quantum fields at two spacetime points, we explore an associated Poisson structure for classical field theories within the deformation quantization formalism. We realize that the induced…
Whenever a given Poisson manifold is equipped with discrete symmetries the corresponding algebra of invariant functions or the algebra of functions twisted by the symmetry group can have new deformations, which are not captured by…
In this review an overview on some recent developments in deformation quantization is given. After a general historical overview we motivate the basic definitions of star products and their equivalences both from a mathematical and a…
In these lecture notes I give an introduction to deformation quantization. The quantization problem is discussed in some detail thereby motivating the notion of star products. Starting from a deformed observable algebra, i.e. the star…
We demonstrated that classical mechanics have, besides the well known quantum deformation, another deformation -- so called hyperbolic quantum mechanics. The classical Poisson bracket can be obtained as the limit $h\to 0$ not only of the…
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…
An unobstructedness theorem is proved for deformations of compact holomorphic Poisson manifolds and applied to a class of examples. These include certain rational surfaces and Hilbert schemes of points on Poisson surfaces. We study in…
We give a simple geometric description of all formal deformation quantizations on a K\"ahler manifold $M$ which enjoy the following property of separation of variables into holomorphic and antiholomorphic ones. For each open subset…
The relation between the Moyal-Weyl deformation quantization and quasiconformal mappings of Riemann surfaces of complex analysis are shown by several examples.
We analyze the Moyal star product in deformation quantization from the resurgence theory perspective. By putting algebraic conditions on Borel transforms, one can define the space of ``algebro-resurgent series'' (a subspace of $1$-Gevrey…
A simple pseudo-Hamiltonian formulation is proposed for the linear inhomogeneous systems of ODEs. In contrast to the usual Hamiltonian mechanics, our approach is based on the use of non-stationary Poisson brackets, i.e. corresponding…
The quantum deformation of the Poisson bracket is the Moyal bracket. We construct quantum deformation of the Dirac bracket for systems which admit global symplectic basis for constraint functions. Equivalently, it can be considered as an…
Deformation quantization of Poisson manifolds is studied within the framework of an expansion in powers of derivatives of Poisson structures. We construct the Lie group associated with a Poisson bracket algebra which defines a second order…
We prove the existence of a deformation quantization for integrable Poisson structures on R^3 and give a generalization for a special class of three dimensional manifolds.
This is a short comment on the Moyal formula for deformation quantization. It is shown that the Moyal algebra of functions on the plane is canonically isomorphic to an algebra of matrices of infinite size.
$C^*$-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…
In the present paper we explicitly construct deformation quantizations of certain Poisson structures on E^*, where E -> M is a Lie algebroid. Although the considered Poisson structures in general are far from being regular or even…
The Fedosov deformation quantization of the symplectic manifold is determined by a 1-form differential r. We identify a class of r for which the $\star$ product becomes the Moyal product by taking appropriate Darboux coordinates, but…
We define and present an example of a deformation quantization product on a Hida space of test functions endowed with a Wick product.
We recall some of the fundamental achievements of formal deformation quantization to argue that one of the most important remaining problems is the question of convergence. Here we discuss different approaches found in the literature so…