Related papers: Is covariant star product unique?
The use of a diffeomorphism covariant star product enables us to construct diffeomorphism invariant gravities on noncommutative symplectic manifolds without twisting the symmetries. As an example, we construct noncommutative deformations of…
Using the Coherent states of many fermionic degrees of freedom labeled by Gra\ss mann variables, we introduce the noncommutative (precisely non anticommutative) Gra\ss mann star product. The covariance of star product under unitary…
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…
The choice of a star product realization for noncommutative field theory can be regarded as a gauge choice in the space of all equivalent star products. With the goal of having a gauge invariant treatment, we develop tools, such as…
We first review the introduction of star products in connection with deformations of Poisson brackets and the various cohomologies that are related to them. Then we concentrate on what we have called ``closed star products" and their…
A formulation of anomalies in terms of star products is suggested which promises insight from an alternative and unifying point of view.
A covariant Poisson bracket and an associated covariant star product in the sense of deformation quantization are defined on the algebra of tensor-valued differential forms on a symplectic manifold, as a generalization of similar structures…
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…
This talk is an introduction to ideas of non-commutative geometry and star products. We will discuss consequences for physics in two different settings: quantum field theories and astrophysics. In case of quantum field theory, we will…
The problem of finding a generic star product on R^n is reduced to the computation of a skew-symmetric biderivation.
In the literature there are two different ways of describing an invariant star product on $S^2$. We show that the products are actually the same. We also calculate the canonical trace and use the Fedosov-Nest-Tsygan index theorem to obtain…
We give an invariant formula for a star product with separation of variables on a pseudo-Kahler manifold.
We study the general form of the noncommutative associative product (the star-product) on the Grassman algebra; the star-product is treated as a deformation of the usual "pointwise" product. We show that up to a similarity transformation,…
The cosmological constant problem represents an evident tension between our present description of gravity and particle physics. Many solutions have been proposed, but experimental tests are always difficult or impossible to perform and…
We develop an internal gauge theory using a covariant star product. The space-time is a symplectic manifold endowed only with torsion but no curvature. It is shown that, in order to assure the restrictions imposed by the associativity…
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…
Covariance of a quantum space with respect to a quantum enveloping algebra ties the deformation of the multiplication of the space algebra to the deformation of the coproduct of the enveloping algebra. Since the deformation of the coproduct…
We construct a weighted version of polyhedral products and compute its cohomology in special cases. This is applied to resolve Steenrod's cohomology realization problem in a case related to products of spheres.
We consider simple extensions of noncommutativity from flat to curved spacetime. One possibility is to have a generalization of the Moyal product with a covariantly constant noncommutative tensor $\theta^{\mu\nu}$. In this case the…
A covariant quantization method is developed for the off-shell superparticle in 10 dimensions. On-shell it is consistent with lightcone quantization, while off-shell it gives a noncommutative superspace that realizes non-linearly a hidden…