Related papers: The Star Product in Interacting Quantum Field Theo…

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…

We construct a star product associated with an arbitrary two dimensional Poisson structure using generalized coherent states on the complex plane. From our approach one easily recovers the star product for the fuzzy torus, and also one for…

Based on work done by Bonechi, Cattaneo, Felder and Zabzine on Poisson sigma models, we formally show that Kontsevich's star product can be obtained from the twisted convolution algebra of the geometric quantization of a Lie 2-groupoid, one…

A new term in the p-adic world-sheet action is proposed, which couples a constant B-field to the boundary of the world-sheet at disk level. The induced deformation of tachyon scattering amplitudes by star-products is derived. This is in…

For every formal power series $B=B_0 + \lambda B_1 + O(\lambda^2)$ of closed two-forms on a manifold $Q$ and every value of an ordering parameter $\kappa\in [0,1]$ we construct a concrete star product $\star^B_\kappa$ on the cotangent…

The framework of perturbative algebraic quantum field theory (pAQFT) is used to construct QFT models on causal sets. We discuss various discretised wave operators, including a new proposal based on the idea of a `preferred past', which we…

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…

Using duality and topological theory of well behaved Hopf algebras (as defined in [2]) we construct star-product models of non compact quantum groups from Drinfeld and Reshetikhin standard deformations of enveloping Hopf algebras of simple…

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…

Let M be a Poisson manifold equipped with a Hermitian star product. We show that any positive linear functional on C^\infty(M) can be deformed into a positive linear functional with respect to the star product.

We make a deformation quantization by Moyal star-product on a space of functions endowed with the normalized Wick product and where Stratonovich chaos are well defined.

Given a holomorphic Hermitian vector bundle and a star-product with separation of variables on a pseudo-Kaehler manifold, we construct a star product on the sections of the endomorphism bundle of the dual bundle which also has the…

We show that the Hochschild cohomology of the algebra obtained by formal deformation quantization on a symplectic manifold is isomorphic to the formal series with coefficients in the de Rham cohomology of the manifold. The cohomology class…

A proposed definition is given for the quantization of a Poisson algebra, taking the quantum product to be a geodesic on the manifold of associative products.

The quantizer-dequantizer formalism is developed for mean value and probability representation of qubits and qutrits. We derive the star-product kernels providing the possibility to derive explicit expressions of the associative product of…

Superanalysis can be deformed with a fermionic star product into a Clifford calculus that is equivalent to geometric algebra. With this multivector formalism it is then possible to formulate Riemannian geometry and an inhomogeneous…

Let $\XR$ be a (generalized) flag manifold of a non-compact real semisimple Lie group $\GR$, where $\XR$ and $\GR$ have complexifications X and G. We investigate the problem of constructing a graded star product on $Pol(T^*\XR)$ which…

This dissertation is an exposition of Kontsevich's proof of the formality theorem and the classification of deformation quantisation on a Poisson manifold. We begin with an account of the physical background and introduce the Weyl-Moyal…

The paper develop the alternative formulation of quantum mechanics known as the phase space quantum mechanics or deformation quantization. It is shown that the quantization naturally arises as an appropriate deformation of the classical…

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…