Related papers: Tensor operators and Wigner-Eckart theorem for U_q…
An ordinary differential operator of the fourth order with coefficients converging at infinity sufficiently rapidly to constant limits is considered. Scattering theory for this operator is developed in terms of special solutions of the…
An approach to study a generalization of the classical-quantum transition for general systems is proposed. In order to develop the idea, a deformation of the ladder operators algebra is proposed that contains a realization of the quantum…
We define quantum phase in terms of inverses of annihilation and creation operators. We show that like Susskind - Glogower phase operators, the measured phase operators and the unitary phase operators can be defined in terms of the inverse…
Free tensors are tensors which, after a change of bases, have free support: any two distinct elements of its support differ in at least two coordinates. They play a distinguished role in the theory of bilinear complexity, in particular in…
We study several classes of indecomposable representations of quivers on infinite-dimensional Hilbert spaces and their relation. Many examples are constructed using strongly irreducible operators. Some problems in operator theory are…
It is shown that the multiquark gauge-invariant operators can, in general, be decomposed into combinations of products of ordinary hadronic operators, exhibiting their cluster reducibility. The latter property inhibits the formation of…
We show that for general deformations of SU(2) algebra, the dynamics in terms of ladder operators is preserved. This is done for a system of precessing magnetic dipole in magnetic field, using the unitary phase operator which arises in the…
Quantum mechanics can be formulated in terms of phase-space functions, according to Wigner's approach. A generalization of this approach consists in replacing the density operators of the standard formulation with suitable functions, the…
An O-operator is a relative version of a Rota-Baxter operator and, in the Lie algebra context, is originated from the operator form of the classical Yang-Baxter equation. We generalize the well-known construction of dendriform dialgebras…
An algebraic representation of the Turing machines is given, where the configurations of Turing machines are represented by 4 order tensors, and the transition functions by 8 order tensors. Two types of tensor product are defined, one is to…
We introduce a weighted de Rham operator which acts on arbitrary tensor fields by considering their structure as r-fold forms. We can thereby define associated superpotentials for all tensor fields in all dimensions and, from any of these…
We show that any arbitrary time-dependent density operator of an open system can always be described in terms of an operator-sum representation regardless of its initial condition and the path of its evolution in the state space, and we…
We find all spin operators for a Dirac particle satisfying the following very general conditions: (i) spin does not convert positive (negative) energy states into negative (positive) energy states, (ii) spin is a pseudo-vector, and (iii)…
By a physical system we recognize a set of propositions about a given system with their truth-values depending on the states of the system. Since every physical system can go from one state in another one, there exists a binary relation on…
Let g be a simple simply laced Lie algebra. In this paper two families of varieties associated to the Dynkin graph of g are described: ``tensor product'' and ``multiplicity'' varieties. These varieties are closely related to Nakajima's…
We analyze the properties of the conditional amplitude operator, the quantum analog of the conditional probability which has been introduced in [quant-ph/9512022]. The spectrum of the conditional operator characterizing a quantum bipartite…
The current paper presents a new approach to multilinear dynamical systems analysis and control. The approach is based upon recent developments in tensor decompositions and a newly defined algebra of circulants. In particular, it is shown…
Invariant tensors play an important role in gauge theories, for example, in dualities of N=1 gauge theories. However, for theories with fields in representations larger than the fundamental, the full set of invariant tensors is often…
A simple version for the extension of the Taylor theorem to the operator functions was found. The expansion was done with respect to a value given by a diagonal matrix for the non-commutative case, and the coefficients are given both by…
We introduce a category $\mathcal O$ of representations of the elliptic quantum group associated with $\mathfrak{sl}_2$ with well-behaved $q$-character theory. We derive separation of variables relations for asymptotic representations in…