Related papers: Quantizing deformation theory II
Deformations of quantum field theories which preserve Poincar\'e covariance and localization in wedges are a novel tool in the analysis and construction of model theories. Here a general scenario for such deformations is discussed, and an…
A quantization of a non-standard rational solution of CYBE for $sl_2$ is given explicitly. We obtain the quantization with the help of a twisting of the usual Yangian $Y(sl_2$. This quantum object (deformed Yangian $Y_{\eta,\xi}(sl_2))$ is…
In this paper we consider the problem of deformation quantization of the algebra of polynomial functions on coadjoint orbits of semisimple lie groups. The deformation of an orbit is realized by taking the quotient of the universal…
We consider non(anti)commutative (NAC) deformations of d=1 N=2 superspace. We find that, in the chiral base, the deformation preserves only a half of the original (linearly realized) supercharge algebra, as it usually happens in NAC field…
Motivated by the representation of the super Virasoro constraints as generalized Dirac-K{\"a}hler constraints $(d \pm d^\dagger)|\psi> = 0$ on loop space, examples of the most general continuous deformations $d \to e^{-W} d e^W$ are…
We introduce dg Lie algebras controlling the deformations of vertex algebras and vertex Poisson algebras, utilizing the notion of operadic dg Lie algebra and the theory of chiral algebra. In terms of those dg Lie algebras, we formulate the…
In this dissertation the notion of deformation quantization of principal fibre bundles is established and investigated in order to find a geometric formulation of classical gauge theories on noncommutative space-times. As a generalization,…
In this article we study the quantization of a free real scalar field on a class of noncommutative manifolds, obtained via formal deformation quantization using triangular Drinfel'd twists. We construct deformed quadratic action functionals…
Quantum deformations of the structure constants for a class of associative noncommutative algebras are studied. It is shown that these deformations are governed by the quantum central systems which has a geometrical meaning of vanishing…
The Cartan-Maurer equations for any $q$-group of the $A_{n-1}, B_n, C_n, D_n$ series are given in a convenient form, which allows their direct computation and clarifies their connection with the $q=1$ case. These equations, defining the…
One way of reconciling classical and quantum mechanics is deformation quantization, which involves deforming the commutative algebra of functions on a Poisson manifold to a non-commutative, associative algebra, reminiscent of the space of…
We present a quantum deformation theory of the Airy curve and use it to establish a version of mirror symmetry of a point.
Is "Gravity" a deformation of "Electromagnetism"? Deformation theory suggests quantizing Special Relativity: formulate Quantum Information Dynamics $SL(2,C)_h$-gauge theory of dynamical lattices, with unifying gauge ``group'' the quantum…
Quantum superintegrable systems in two dimensions are obtained from their classical counterparts, the quantum integrals of motion being obtained from the corresponding classical integrals by a symmetrization procedure. For each quantum…
We make use of a well-know deformation of the Poincar\'e Lie algebra in $p+q+1$ dimensions ($p+q>0$) to construct the Poincar\'e Lie algebra out of the Lie algebras of the de Sitter and anti de Sitter groups, the generators of the…
We consider the $T\bar{T}$ deformation of two dimensional Yang--Mills theory on general curved backgrounds. We compute the deformed partition function through an integral transformation over frame fields weighted by a Gaussian kernel. We…
Firstly we discuss different versions of noncommutative space-time and corresponding appearance of quantum space-time groups. Further we consider the relation between quantum deformations of relativistic symmetries and so-called doubly…
We investigate the application of deformation quantization to the system of a free particle evolving within a universe described by a Friedmann-Lemaitre-Robertson-Walker (FLRW) geometry. This approach allows us to analyze the dynamics of…
Based on the idea of quantum groups and paragrassmann variables, we presenta generalization of supersymmetric classical mechanics with a deformation parameter $q= \exp{\frac{2 \pi i}{k}}$ dealing with the $k =3$ case. The coordinates of the…
In this work we give a deformation theoretical approach to the problem of quantization. First the notion of a deformation of a noncommutative ringed space over a commutative locally ringed space is introduced within a language coming from…