Related papers: General approach to SU(n) quasi-distribution funct…
The meaning of quantum group transformation properties is discussed in some detail by comparing the (co)actions of the quantum group with those of the corresponding Lie group, both of which have the same algebraic (matrix) form of the…
We formulate the notion of equivariance of an operator with respect to a covariant representation of a C^*-dynamical system. We then use a combinatorial technique used by the authors earlier in characterizing spectral triples for SU_q(2) to…
Complex numbers appear in the Hilbert space formulation of quantum mechanics, but not in the formulation in phase space. Quantum symmetries are described by complex, unitary or antiunitary operators defining ray representations in Hilbert…
The method of geometrical quantization of symplectic manifolds is applied to constructing infinite dimensional irreducible unitary representations of the algebra of functions on the compact quantum group $SU_q(2)$. A formulation of the…
This paper establishes a link between Noncommutative Geometry and canonical quantum gravity. A semi-finite spectral triple over a space of connections is presented. The triple involves an algebra of holonomy loops and a Dirac type operator…
We construct the system of generalized coherent states for the quantum Kepler problem corresponds to the homogeneous domain $SU(2,2)/S(U(2)\times U(2))$. We show that the SU(2,2)-equivariant momentum map for this domain yields the momentum…
We describe a method to perform functional operations on probability distributions of random variables. The method uses reproducing kernel Hilbert space representations of probability distributions, and it is applicable to all operations…
Semiclassical periodic-orbit theory and closed-orbit theory represent a quantum spectrum as a superposition of contributions from individual classical orbits. Close to a bifurcation, these contributions diverge and have to be replaced with…
In the present paper, we consider the integral operator, which acts in Hilbert space and has sine kernel. This operator generates two operator identities and two corresponding canonical differential systems. We find the asymptotics of the…
We provide a holomorphic description of the Hilbert space H(j_1,..,j_n) of SU(2)-invariant tensors (intertwiners) and establish a holomorphically factorized formula for the decomposition of identity in H(j_1,..,j_n). Interestingly, the…
A new functional calculus, developed recently for a fully non-perturbative treatment of quantum gravity, is used to begin a systematic construction of a quantum theory of geometry. Regulated operators corresponding to areas of 2-surfaces…
We start by showing how to approximate unitary and bounded self-adjoint operators by operators in finite dimensional spaces. Using ultraproducts we give a precise meaning for the approximation. In this process we see how the spectral…
We consider the quantum mechanics of a particle on a noncommutative two-sphere with the coordinates obeying an SU(2)-algebra. The momentum operator can be constructed in terms of an $SU(2)\times SU(2)$-extension and the Heisenberg algebra…
The review of star-product formalism providing the possibility to describe quantum states and quantum observables by means of the functions called symbols of operators which are obtained by means of bijective maps of the operators acting in…
We derive an intuitive and novel method to represent nodes in a graph with special unitary operators, or quantum operators, which does not require parameter training and is competitive with classical methods on scoring similarity between…
Motivated by the recent developments of pseudo-hermitian quantum mechanics, we analyze the structure of unbounded metric operators in a Hilbert space. It turns out that such operators generate a canonical lattice of Hilbert spaces, that is,…
In this note we study half-BPS operators in N=4 super Yang-Mills for gauge group SU(N) at finite N. In particular we elaborate on the results of hep-th/0410236, providing an exact formula for the null basis operators algorithmically…
Supersymmetric quantum mechanics is constructed in a new non-Hermitian representation. Firstly, the map between the partner operators $H^{(\pm)}$ is chosen antilinear. Secondly, both these components of a super-Hamiltonian ${\cal H}$ are…
Algebraic models are proposed for the description of the shell-like quarteting of the nucleons both on the phenomenologic and on the semimicroscopic levels. In the previous one the quartet is considered as a structureless object, while in…
In many instances one has to deal with parametric models. Such models in vector spaces are connected to a linear map. The reproducing kernel Hilbert space and affine- / linear- representations in terms of tensor products are directly…