Related papers: On the Associativity of Star Product in Systems wi…
The deformation quantization by Kontsevich [arXiv:q-alg/9709040] is a way to construct an associative noncommutative star-product $\star=\times+\hbar \{\ ,\ \}_{P}+\bar{o}(\hbar)$ in the algebra of formal power series in $\hbar$ on a given…
In his celebrated paper Kontsevich has proved a theorem which manifestly gives a quantum product (deformation quantization formula) and states that changing coordinates leads to gauge equivalent star products. To illuminate his procedure,…
We propose an explicit construction of the deformation quantization of the general second-class constrained system, which is covariant with respect to local coordinates on the phase space. The approach is based on constructing the effective…
The star product technique translates the framework of local fields on noncommutative space-time into nonlocal fields on standard space-time. We consider the example of fields on $\kappa$- deformed Minkowski space, transforming under…
We construct a multiple star product method and by using this method, show that integral forms of some star products can be written in terms of the path-integral. This method can be applied to some examples. Especially, the associativity of…
Some physical systems like the quantum mechanics with magnetic charges or field theoretical models appearing in the context of string theory are formulated in terms of non-associative algebras. Hence, demand non-associative star products…
The formality morphism $\boldsymbol{\mathcal{F}}=\{\mathcal{F}_n$, $n\geqslant1\}$ in Kontsevich's deformation quantization is a collection of maps from tensor powers of the differential graded Lie algebra (dgLa) of multivector fields to…
It is well known that for a given Poisson structure one has infinitely many star products related through the Kontsevich gauge transformations. These gauge transformations have an infinite functional dimension (i.e., correspond to an…
We review two known in the literature exemples of non-associative star products. The first one is the phase space star product representing quantization of non-geometric $R$-flux background in closed string theory. The second is the…
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…
We show that there is an obstruction to the existence of a star product defined by Kontsevich graphs without directed cycles.
In this paper, we formulate the phase space description of qubit systems using coadjoint orbits of $SU(2)$ and the Stratonovich-Weyl correspondence, yielding a deformation quantization on the sphere. The resulting star product reproduces…
In the present paper we prove a statement closely related to the cyclic formality conjecture. In particular, we prove that for a divergence-free Poisson bivector field on R^d, the Kontsevich star-product with the harmonic angle function is…
The quantization of the second-class constraint systems is discussed within the projection operator method(POM) of constraint systems. Through the nonlocal representation of the constraint hyper-operators, new star-products are defined.…
We consider the bounded linear operators with domain in the Hilbert space $L^2(S^n)$, $n=2,3,5$ and describe its symbolic calculus defined by the Berezin quantization. In particular, we derive an explicit formula for the composition of…
Non-commutativity and non-associativity are quite natural in string theory. For open strings it appear due to the presence of non-vanishing background two-form in the world volume of Dirichlet brane, while in closed string theory the flux…
Adopting a purely group-theoretical point of view, we consider the star product of functions which is associated, in a natural way, with a square integrable (in general, projective) representation of a locally compact group. Next, we show…
The formula $\star$ mod $\bar{o}(\hbar^k)$ of Kontsevich's star-product with harmonic propagators was known in full at $\hbar^{k\leqslant 6}$ since 2018 for generic Poisson brackets, and since 2022 also at $k=7$ for affine brackets. We…
In the present paper we construct the star products concerning scalar fields in the covariant case from a new approach. We construct the star products at three levels, which are levels of functions on Rd, fields and functionals…
It is shown that a (curved) projective structure on a smooth manifold determines on the Poisson algebra of smooth, fiberwise-polynomial functions on the cotangent bundle a one-parameter family of graded star products. For a particular value…