Related papers: Spin Connections and Classification of Inequivalen…
We give an elementary introduction to the notion of quantum entanglement between distinguishable parties and review a recent proposal about solid state quantum computation with spin-qubits in quantum dots. The indistinguishable character of…
A consistent procedure of canonical quantization of pseudoclassical model for spin one relativistic particle is considered. Two approaches to treat the quantization for the massless case are discussed, the limit of the massive case and…
In this paper we introduce the concept of Hamiltonian system in the canonical and Poisson settings. We will discuss the quantization of the Hamiltonian systems in the Poisson context, using formal deformation quantization and quantum group…
In this paper we consider the representation theory of a non-standard quantization of sl(2). This paper contains several results which have applications in quantum topology, including the classification of projective indecomposable modules…
Quantum mechanics on manifolds is not unique and in general infinite number of inequivalent quantizations can be considered. They are specified by the induced spin and the induced gauge structures on the manifold. The configuration space of…
We present an interpretation of loop quantization in the framework of lattice gauge theory. Within this context the lack of appropriate notions of effective theories and renormalization group flow exhibit loop quantization as an incomplete…
We review several known categorification procedures, and introduce a functorial categorification of group extensions with applications to non-abelian group cohomology. Categorification of acyclic models and of topological spaces are briefly…
We develop an abstract framework for the investigation of quantization and dequantization procedures based on orthogonality relations that do not necessarily involve group representations. To illustrate the usefulness of our abstract method…
We discuss the notion of linearization through examples, which include the Price map, PageRank, representation theory, the Euler characteristic and quantum invariants. We also review categorification, which adds an additional layer of…
The paper is devoted to integral quantization, a procedure based on operator-valued measure and resolution of the identity. We insist on covariance properties in the important case where group representation theory is involved. We also…
The classical soliton solution, quantized by means of suitable translational and rotational collective coordinates, is embedded into the one-particle irreductible representation of the Poincare group corresponding to a definite spin. It is…
Taking the XXZ chain as the main example, we give a review of an algebraic representation of correlation functions in integrable spin chains obtained recently. We rewrite the previous formulas in a form which works equally well for the…
We present two results on the recently proposed new spin foam models. First, we show how a (slightly modified) restriction on representations in the EPRL model leads to the appearance of the Ashtekar-Barbero connection, thus bringing this…
Drawing on well-known results from the theory of canonical extensions and the theory of categories enriched over a quantale, we define canonical extensions of quantale-enriched categories and establish their basic properties.
We categorify one half of the small quantum sl(2) at a prime root of unity. An extension of this construction to an arbitrary simply-laced case is proposed.
We construct the augmentation representation. It is a representation of the fundamental group of the link complement associated to an augmentation of the framed cord algebra. This construction connects representations of two link invariants…
We carry out a generalization of quantum group co-representations in order to encode in this structure those cases where non-commutativity between endomorphism matrix entries and quantum space coordinates happens.
A pseudoclassical model, reproducing, upon quantization, the dynamics of the chiral sectors of the massless spin-1/2 field theory is proposed. The discrete symmetries of the action are studied in details. In order to reproduce the positive…
We consider spin system defined on the coadjoint orbit with noncompact symmetry and investigate the quantization. Classical spin with noncompact SU(N,1) symmetry is first formulated as a dynamical system and the constraint analysis is…
We quantize a relativistic massive complex spin-0 field and a relativistic massive spin-1/2 field on a space-time hyperboloid. We call this procedure point-form canonical quantization. Lorentz invariance of the hyperboloid implies that the…