Related papers: Exhausting formal quantization procedures
We introduce three generalizations of homotopy equivalence in digital images, to allow us to express whether a finite and an infinite digital image are similar with respect to homotopy. We show that these three generalizations are not…
Stability and stabilization for linear state feedback control systems in the presence of sensor quantization are studied. As the closed-loop system is described by a discontinuous right-hand side differential equation, Krasovskii solutions…
We give a complete list of formal invariants for a large class of formal differential 1-forms $\w \in \Bbb C [[ x, y]]dx + \Bbb C [[ x, y]]dy$. \indent A $\hat{SL}$-equisingular deformation is an equireducible deformation which leaves…
We give elementary applications of quasi-homomorphisms to growth problems in groups. A particular case concerns the number of torsion elements required to factorise a given element in the mapping class group of a surface.
We study a generalization of the isomonodromic deformation to the case of connections with irregular singularities. We call this generalization Isostokes Deformation. A new deformation parameter arises: one can deform the formal normal…
We study the class of all algebras that are isotopic to a Hurwitz algebra. Isomorphism classes of such algebras are shown to correspond to orbits of a certain group action. A complete, geometrically intuitive description of the category of…
In this paper, we try to generalise quantum stabilizer formalism to any composite system, that is, it includes not only composite systems of equal dimensions, but also composite systems of unequal dimensions.
The paper introduces and studies the notions of Lipschitzian and H\"olderian full stability of solutions to three-parametric variational systems described in the generalized equation formalism involving nonsmooth base mappings and partial…
We study the category of algebras of substitudes (also known to be equivalent to the regular patterns of Getzler) equipped with a (semi)model structure lifted from the model structure on the underlying presheaves. We are especially…
It is shown here and in the preceeding paper (quant-ph/0201129) that vector coherent state theory, the theory of induced representations, and geometric quantization provide alternative but equivalent quantizations of an algebraic model. The…
These are notes from an informal mini-course on factorization homology, infinity-categories, and topological field theories. The target audience was imagined to be graduate students who are not homotopy theorists.
It is constructed a formal normal form, using an iterative normalization procedure, for a large class of Real-Smooth Hypersurfaces in Complex Spaces.
We prove that either the images of the mapping class groups by quantum representations are not isomorphic to higher rank lattices or else the kernels have a large number of normal generators. Further we show that the images of the mapping…
We identify Drinfeld's formal group on the prismatization of $\mathrm{Spf}\,\mathbb{Z}_p$ with a formal group arising from homotopy theory, given locally by the Quillen formal group of a decompleted variant of topological periodic cyclic…
This note describes the functional-integral quantization of two-dimensional topological field theories together with applications to problems in deformation quantization of Poisson manifolds and reduction of certain submanifolds. A brief…
In this paper, we mainly focus on formal deformation theory of module homomorphisms. We first introduce the cohomology of module homomorphisms and study formal one-parameter deformation. We obtain some properties about obstructions. Then we…
This set of notes corresponds to a mini-course given in September 2018 in Bedlewo; it does not contain any new result; it complements -- with intersection -- the introduction to formal deformation quantization and group actions,…
The goal of this paper is to present a formalism that allows to handle four-fermion effective theories at finite temperature and density in curved space. The formalism is based on the use of the effective action and zeta function…
A covariant quantization scheme employing reducible representations of canonical commutation relations with positive-definite metric and Hermitian four-potentials is tested on the example of quantum electrodynamic fields produced by a…
Let $f: X \to Y$ be a regular covering of a surface $Y$ of finite type with nonempty boundary, with finitely-generated (possibly infinite) deck group $G$. We give necessary and sufficient conditions for an integral homology class on $X$ to…