Related papers: Fedosov *-products and quantum momentum maps
We study a quantum moment map and propose an invariant for $G$-invariant star products on a $G$-transitive symplectic manifold. We start by describing a new method to construct a quantum moment map for $G$-invariant star products of Fedosov…
In these notes we consider the usual Fedosov star product on a symplectic manifold $(M,\omega)$ emanating from the fibrewise Weyl product $\circ$, a symplectic torsion free connection $\nabla$ on M, a formal series $\Omega \in \nu…
Fedosov has described a geometro-algebraic method to construct in a canonical way a deformation of the Poisson algebra associated with a finite-dimensional symplectic manifold ("phase space"). His algorithm gives a non-commutative, but…
We define a natural class of star products: those which are given by a series of bidifferential operators which at order $k$ in the deformation parameter have at most $k$ derivatives in each argument. We show that any such star product on a…
We study quantum moment maps of $G$-invariant star products, which are a quantum analogue of the moment map for classical Hamiltonian systems. Introducing an integral representation, we show that any quantum moment map for a $G$-invariant…
This is an expository note on Fedosov's construction of deformation quantization. Given a symplectic manifold and a connection on it, we show how to calculate the star-product step by step. We draw simple diagrams to solve the recursive…
In an interesting work M.F. Muller-Bahns and N. Neumaier ("Some remarks on g-invariant Fedosov star products and quantum momentum mappings". Journal of Geometry and Physics 50 (2004), 257-272.) analyze the existence of a quantum momentum…
The construction of the *-product proposed by Fedosov is implemented in terms of the theory of fibre bundles. The geometrical origin of the Weyl algebra and the Weyl bundle is shown. Several properties of the product in the Weyl algebra are…
We deform the moment map picture on the space of symplectic connections on a symplectic manifold. To do that, we study a vector bundle of Fedosov star product algebras on the space of symplectic connections. We describe a natural formal…
We extend our investigations on $\mathfrak g$-invariant Fedosov star products and quantum momentum mappings \cite{MN03a} to star products of Wick type on pseudo-K\"ahler manifolds. Star products of Wick type can be completely characterized…
Multisymplectic geometry admits an operation that has no counterpart in symplectic geometry, namely, taking the product of two multisymplectic manifolds endowed with the wedge product of the multisymplectic forms. We show that there is an…
We study the Cahen-Gutt moment map on the space of symplectic connections of a symplectic manifold. On a K\"ahler manifold, we define a Calabi-type functional $\mathscr{F}$ on the space of K\"ahler metrics in a given K\"ahler class. We…
For a compact Lie group $G$ we consider a lattice gauge model given by the $G$-Hamiltonian system which consists of the cotangent bundle of a power of $G$ with its canonical symplectic structure and standard moment map. We explicitly…
Invertible maps from operators of quantum obvservables onto functions of c-number arguments and their associative products are first assessed. Different types of maps like Weyl-Wigner-Stratonovich map and s-ordered quasidistribution are…
Hamiltonians whose symbols are not simply real valued, but matrix or, more generally, endomorphism valued functions appear in many places in physics, examples being the Dirac equation, multicomponent wave equations like electrodynamics in…
Some properties of the star product of the Weyl type (i.e. associated with the Weyl ordering) are proved. Fedosov construction of the *-product on a 2-dimensional phase spacewith a constant curvature tensor is presented. Eigenvalue…
We review our construction of star-products on Poisson manifolds and discuss some examples. In particular, we work out the relation with Fedosov's original construction in the symplectic case.
In this note we classify invariant star products with quantum momentum maps on symplectic manifolds by means of an equivariant characteristic class taking values in the equivariant cohomology. We establish a bijection between the…
It is shown that the normalized trace of Fedosov star product for quantum moment map depends only on the path component in the cohomology class of the symplectic form and the cohomology class of the closed formal 2-form required to define…
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…