Related papers: Abelian connection in Fedosov deformation quantiza…
The topic of this paper are (multi-window) Gabor frames for signals over finite Abelian groups, generated by an arbitrary lattice within the finite time-frequency plane. Our generic approach covers simultaneously multi-dimensional signals…
We begin the study of completeness of affine connections, especially those on statistical manifolds as well as on affine hypersurfaces. We collect basic facts, prove new theorems and provide examples with remarkable properties.
We discuss recent results on bosonization in $d \geq 2$ space-time dimensions by giving a very simple derivation for the bosonic representation of the original free fermionic model both in the abelian and non-abelian cases. We carefully…
Fedosov has described a geometro-algebraic method to construct in a canonical way a deformation of the Poisson algebra associated with a finite-dimensional symplectic manifold ("phase space"). His algorithm gives a non-commutative, but…
In this paper we give a construction of Fedosov quantization incorporating the odd variables and an analogous formula to Getzler's pseudodifferential calculus composition formula is obtained. A Fedosov type connection is constructed on the…
We define a universal deformation formula (UDF) for the actions of the affine group on Frechet algebras. More precisely, starting with any associative Frechet algebra which the affine group acts on in a strongly continuous and isometrical…
We classify the category of finite-dimensional real division composition algebras having a non-abelian Lie algebra of derivations. Our complete and explicit classification is largely achieved by introducing the concept of a…
We introduce a notion of elliptic differential graded Lie algebra. The class of elliptic algebras contains such examples as the algebra of differential forms with values in endomorphisms of a flat vector bundle over a compact manifold, etc.…
A complete classification and character formulas for finite-dimensional irreducible representations of the rational Cherednik algebra of type A is given. Less complete results for other types are obtained. Links to the geometry of affine…
We study some natural connections on spaces of conformal field theories using an analytical regularization method. The connections are based on marginal conformal field theory deformations. We show that the analytical regularization…
We start with a short exposition of developments in physics and mathematics that preceded, formed the basis for, or accompanied, the birth of deformation quantization in the seventies. We indicate how the latter is at least a viable…
The quantum completion of the space of connections in a manifold can be seen as the set of all morphisms from the groupoid of the edges of the manifold to the (compact) gauge group. This algebraic construction generalizes an analogous…
In canonical gravity, general covariance is implemented by hypersurface-deformation symmetries on phase space. The different versions of hypersurface deformations required for full covariance have complicated interplays with one another,…
Given a fibration over the circle, we relate the eigenspace decomposition of the algebraic monodromy, the homological finiteness properties of the fiber, and the formality properties of the total space. In the process, we prove a more…
In this note some properties of the sum of element orders of a finite abelian group are studied.
The Epstein deformation space parameterizes marked rational maps with prescribed combinatorial and dynamical structure. For the family of quadratic rational maps with a periodic critical cycle of order 4 and an extra critical point not…
An abelian version of standard general relativity in the Cartan-Palatini gauge-like formulation in four dimensions has been introduced. Traditional canonical analysis utilizing similarities to the akin Husain-Kuchar SU(2) version of gravity…
We present finitary formulations of two well known results concerning infinite series, namely Abel's theorem, which establishes that if a series converges to some limit then its Abel sum converges to the same limit, and Tauber's theorem,…
We consider a real manifold of dimension 3 or 4 with Minkovsky metric, and with a connection for a trivial GL(n,C) bundle over that manifold. To each light ray on the manifold we assign the data of paralel transport along that light ray. It…
We characterize quotient of a non-degenerate abelian fibration by a finite \'etale equivalence relation. We show that non-uniruled degenerations of each such quotient tend to be almost non-degenerate.