Related papers: Quantizing deformation theory II
It is a basic introduction to differential graded Lie algebras, Maurer-Cartan equation and associated deformation functors.
Deformation Theory is a natural generalization of Lie Theory, from Lie groups and their linearization, Lie algebras, to differential graded Lie algebras and their higher order deformations, quantum groups. The article focuses on two basic…
In this work, we present straightforward and concrete computations of the unitary irreducible representations of the Euclidean motion group $M(2)$ employing the methods of deformation quantization. Deformation quantization is a quantization…
The aim of this proceeding is to give a basic introduction to Deformation Quantization (DQ) to physicists. We compare DQ to canonical quantization and path integral methods. It is described how certain issues such as the roles of…
Deformation quantization (the Moyal deformation) of SDYM equation for the algebra of the area preserving diffeomorphisms of a 2-surface $\Sigma_{2}$, sdiff($\Sigma_{2}$), is studied. Deformed equation we call the master equation (ME) as it…
First three sections of this overview paper cover classical topics of deformation theory of associative algebras and necessary background material. We then analyze algebraic structures of the Hochschild cohomology and describe the relation…
We review several procedures of quantization formulated in the framework of (classical) phase space M. These quantization methods consider Quantum Mechanics as a "deformation" of Classical Mechanics by means of the "transformation" of the…
Deformations of the 3-differential of 3-differential graded algebras are controlled by the (3,N) Maurer-Cartan equation. We find explicit formulae for the coefficients appearing in that equation, introduce new geometric examples of…
The Batalin-Vilkovisky master equations, both classical and quantum, are precisely the integrability equations for deformations of algebras and differential algebras respectively. This is not a coincidence; the Batalin-Vilkovisky approach…
An approach to study a generalization of the classical-quantum transition for general systems is proposed. In order to develop the idea, a deformation of the ladder operators algebra is proposed that contains a realization of the quantum…
We study an algebraic deformation problem which captures the data of the general deformation problem for a quantum vertex algebra. We derive a system of coupled equations which is the counterpart of the Maurer-Cartan equation on the usual…
The aim of these notes is to introduce the quantum master equation $\{S,S\}-2i\hbar\Delta S=0$, and to show its relations to the theory of Lie algebras representations and to perturbative expansions of Gaussian integrals. The relations of…
We consider the deformations of a supersymmetric quantum field theory by adding spacetime-dependent terms to the action. We propose to describe the renormalization of such deformations in terms of some cohomological invariants, a class of…
We consider deformed special relativity (DSR) theories on commutative space-time, perhaps as an first approximation to a noncommutative space-time formulation. The corresponding field theories in general possess derivatives of all orders.…
Second quantization of a classical nonrelativistic one-particle system as a deformation quantization of the Schrodinger spinless field is considered. Under the assumption that the phase space of the Schrodinger field is $C^{\infty}$, both,…
In these lecture notes I give an introduction to deformation quantization. The quantization problem is discussed in some detail thereby motivating the notion of star products. Starting from a deformed observable algebra, i.e. the star…
This paper studies the quantization of the deformation of Hessian structures on a two-dimensional vector space, in the framework of Koszul-Vinberg algebras. We analyze how Hessian structures can be deformed to obtain quantum structures…
We construct a deformation of the quantum algebra Fun(T^*G) associated with Lie group G to the case where G is replaced by a quantum group G_q which has a bicovariant calculus. The deformation easily allows for the inclusion of the current…
The aim of this paper is to give a basic overview of Deformation Quantization (DQ) to physicists. A summary is given here of some of the key developments over the past thirty years in the context of physics, from quantum mechanics to…
The limiting transitions between different types of quantizations are studied by the deformation theory methods. We prove that for the first order coboundary deformation (g,g*_1 + x g*_2) of a Lie bialgebra (g,g*) one can always get the…