Related papers: Deformation quantization with generators and relat…

We propose an exercise in which one attempts to deduce the formalism of quantum mechanics solely from phenomenological observations. The only assumed inputs are the multi-time probability distributions estimated from the results of…

In the paper we formulate and verify a difference counterpart of the Macdonald-Mehta conjecture and its generalization for the Macdonald polynomials. Namely, we determine the Fourier transforms of the polynomials multiplied by the Gaussian,…

In this paper we complete the proof of Caldararu's conjecture on the compatibility between the module structures on differential forms over poly-vector fields and on Hochschild homology over Hochschild cohomology. In fact we show that…

We study the von Neumann algebra generated by q--deformed Gaussian elements l_i+l_i^* where operators l_i fulfill the q--deformed canonical commutation relations l_i l_j^*-q l_j^* l_i=delta_{ij} for -1<q<1. We show that if the number of…

Inspired by the work of Wang and Zhou [4] for Rota-Baxter algebras, we develop a cohomology theory of Rota-Baxter systems and justify it by interpreting the lower degree cohomology groups as formal deformations and as abelian extensions of…

The motivation of this paper is to construct a deformation theory of coderivations of coassociative coalgebras. We introduce a notion of a Coder pair, that is, a coassociative coalgebra with a coderivation. Then we define a proper…

We prove the equivalence of two presentations of deformed double current algebras associated to a complex simple Lie algebra, the first one obtained via a degeneration of affine Yangians while the other one naturally appeared in the…

In this paper, we prove that any two birational projective varieties with finite quotient singularities can be realized as two geometric GIT quotients of a non-singular projective variety by a reductive algebraic group. Then, by applying…

In the companion paper arXiv:2110.05298, we developed the deformation theory of symplectic foliations, focusing on geometric aspects. Here, we address some algebraic questions that arose naturally. We show that the $L_{\infty}$-algebra…

Affine transformations (dilatations and translations) are used to define a deformation of one-dimensional $N=2$ supersymmetric quantum mechanics. Resulting physical systems do not have conserved charges and degeneracies in the spectra.…

This is a survey of the relationship between C*-algebraic deformation quantization and the tangent groupoid in noncommutative geometry, emphasizing the role of index theory. We first explain how C*-algebraic versions of deformation…

Using bicomplex formalism we construct generalizations of Fordy-Kulish systems of matrix nonlinear Schroedinger equations on two-dimensional space-time in two respects. Firstly, we obtain corresponding equations in three space-time…

We formulate and prove a Riemann-Hilbert correspondence between $\hbar$-differential equations and sheaf quantizations, which can be considered as a correspondence between two kinds of quantizations (deformation and sheaf quantization) of…

After sketching recent advances and subtleties in classical relativistically covariant field theories, we give in this short Note some indications as to how the deformation quantization approach can be used to solve or at least give a…

Let $V$ be a finite dimensional real vector space. In the article we construct an isomorphism between the space of smooth translation invariant valuations on convex subsets of $V$ and the space of such valuations (twisted by densities) on…

We prove that small deformations of a projective variety of general type are also projective varieties of general type, with the same plurigenera. Version 2: small changes in first half. Improved version of the second half is now a separate…

In this paper we describe the effect on quantum groups -- namely, both QUEA's and QFSHA's -- of deformations by twist and by 2-cocycles, showing how such deformations affect the semiclassical limit. As a second, more important task, we…

A new approach to deformation quantization on the cylinder considered as phase space is presented. The method is based on the standard Moyal formalism for R^2 adapted to (S^1 x R) by the Weil--Brezin--Zak transformation. The results are…

We study arithmetic properties of factorizations of elements into products of generators, in monoids given with explicit presentations. After relating and comparing this perspective to the more usual approach of factoring into products of…

We summarise the chain of comparisons showing Hinich's derived Maurer-Cartan functor gives an equivalence between differential graded Lie algebras and derived Schlessinger functors on Artinian differential graded-commutative algebras. We…