Related papers: Quantum SL(3,C)'s with classical representation th…
A non-classical, non-quantum theory, or NCQ, is any fully consistent theory that differs fundamentally from both the corresponding classical and quantum theories, while exhibiting certain features common to both. Such theories are of…
For each odd prime power $q$ with $q\ge 5$ and $4\mid q-1$, we investigate the structure of the representation category of the quantum double of ${\rm SL}(2,q)$, determining its tensor products and braidings.
We investigate the rigidity and asymptotic properties of quantum SU(2) representations of mapping class groups. In the spherical braid group case the trivial representation is not isolated in the family of quantum SU(2) representations. In…
We study the category $\mathcal{A}$ of smooth semilinear representations of the infinite symmetric group over the field of rational functions in infinitely many variables. We establish a number of results about the structure of…
Quantum spaces with $\frak{su}(2)$ noncommutativity can be modelled by using a family of $SO(3)$-equivariant differential $^*$-representations. The quantization maps are determined from the combination of the Wigner theorem for $SU(2)$ with…
There are theories of coverings of $C^*$-algebras which can be included into a following list: coverings of commutative $C^*$-algebras, coverings of $C^*$-algebras of groupoids and foliations, coverings of noncommutative tori, the double…
The convenience of coherent state representation is discussed from the viewpoint of what is in a broad sense called the measurement problem in quantum mechanics. Standard quantum theory in coherent state representation is intrinsically…
The categories of representations of compact quantum groups of automorphisms of certain inclusions of finite dimensional C*-algebras are shown to be isomorphic to the categories of Fuss-Catalan diagrams.
Given a quantum graph $ \Gamma $, a finite symmetry group $ G $ acting on it and a representation $ R $ of $ G $, the quotient quantum graph $ \Gamma /R $ is described and constructed in the literature [1, 2, 18]. In particular, it was…
In this article we present a characterization of elliptic curves defined over a finite field Fq which possess a rational subgroup of order three. There are two posible cases depending on the rationality of the points in these groups. We…
We review a geometric approach to classification and examination of quantum correlations in composite systems. Since quantum information tasks are usually achieved by manipulating spin and alike systems or, in general, systems with a finite…
We construct representations of the quantum algebras ~$U_{q{\bf q}}(gl(n))$ and ~$U_{q{\bf q}}(sl(n))$~ which are in duality with the multiparameter quantum groups ~$GL_{q{\bf q}}(n)$, ~$SL_{q{\bf q}}(n)$,~ respectively. These objects…
We study space-time symmetries in scalar quantum field theory (including interacting theories) on static space-times. We first consider Euclidean quantum field theory on a static Riemannian manifold, and show that the isometry group is…
The definitions of classical and quantum singularities in general relativity are reviewed. The occurence of quantum mechanical singularities in certain spherically symmetric and cylindrically symmetric (including infinite line…
This paper is a sequel to our previous study of spherical representations in the operator algebra setup. We first introduce possible analogs of dimension groups in the present context by utilizing the notion of operator systems and their…
Testing the symmetries of quantum states and channels provides a way to assess their usefulness for different physical, computational, and communication tasks. Here, we establish several complexity-theoretic results that classify the…
We review the classical and quantum singularity structure of a broad class of spacetimes with asymptotically power-law behavior near the origin. Quantum considerations "heal" a large class of scalar curvature singularities.
We discuss existence of mixed state of multicomponent system with given spectrum and given reduced density matrices. We give a complete solution of the problem in terms of linear inequalities on the spectra, accompanied with extensive…
We present the characterizations of symbol correspondences for mechanical systems that are symmetric by $SU(3)$, which we refer to as \emph{quark systems}. The quantum quark systems are the unitary irreducible representations of $SU(3)$ of…
A class of quantum analogues of compact symmetric spaces of classical type is introduced by means of constant solutions to the reflection equations. Their zonal spherical functions are discussed in connection with $q$-orthogonal…