Related papers: Representations and Properties of Generalized $A_r…
Starting with an operator in the universal enveloping algebra of a semi-simple, complex Lie group the nearest neighbor statistics of the spectra of this operator along a sequence of representations are discussed. After a short introduction…
A factor-graph representation of quantum-mechanical probabilities (involving any number of measurements) is proposed. Unlike standard statistical models, the proposed representation uses auxiliary variables (state variables) that are not…
An exposition of the different definitions and approaches to quantum statistics is given, with emphasis in one-dimensional situations. Permutation statistics, scattering statistics and exclusion statistics are analyzed. The Calogero model,…
In the present article the author extends the Fourier transform to a more general class of functions; First to power-law functions with integer and half-integer exponents then to the widely used quantum statistics function (Fermi-Dirac and…
We study a certain family of finite-dimensional simple representations over quantum affine superalgebras associated to general linear Lie superalgebras, the so-called fundamental representations: the denominators of rational $R$-matrices…
We review generalizations of quantum statistics, including parabose, parafermi, and quon statistics, but not including anyon statistics, which is special to two dimensions.
To a representation of $\O_N$ (the Cuntz algebra with $N$ generators) we associate a projection valued measure and we study the case when this measure has atoms. The main technical tool are the spaces invariant for all the operators…
The concept of exchange braid statistics is generalized. The cross statistics is studied as a result of interaction. An algebraic model of a system of particles equipped with such statistics is described. The corresponding Fock space…
In any given experimental scenario, the rules of quantum theory provide statistical distributions that the observed outcomes are expected to follow. The set formed by all these distributions contains the imprint of quantum theory, capturing…
Generalized Intelligent States (coherent and squeezed states) are derived for an arbitrary quantum system by using the minimization of the so-called Robertson-Schr\"odinger uncertainty relation. The Fock-Bargmann representation is also…
Application of the so-called refined algebraic quantization scheme for constrained systems to the relativistic particle provides an inner product that defines a unique Fock representation for a scalar field in curved space-time. The…
A system of interacting atoms is represented as an union of two subsystems, one of which is the system of atoms, and the other is an auxiliary scalar covariant field, which is equivalent to a given static interatomic potential of general…
By considering generalized logarithm and exponential functions used in nonextensive statistics, the four usual algebraic operators : addition, subtraction, product and division, are generalized. The properties of the generalized operators…
The aim of the paper is to derive essential elements of quantum mechanics from a parametric structure extending that of traditional mathematical statistics. The main extensions, which also can be motivated from an applied statistics point…
We study Sorkin's proposal of a generalization of quantum mechanics and find that the theories proposed derive their probabilities from $k$-th order polynomials in additive measures, in the same way that quantum mechanics uses a probability…
A description of the quantum superalgebra U_q[sl(n+1|m)] via creation and annihilation generators (CAGs) is given. A statement that the Fock representations of the CAGs provide microscopic realizations of exclusion statistics is formulated.
Usual quantum statistics is written in Fock space but it is not an algebraic theory. We show that at a deeper level it can be algebraically formalized defining the different statistics as (multi-mode) coherent states of the appropriate (but…
As an alternative to Chevalley generators, we introduce Jacobson generators for the quantum superalgebra $U_q[sl(n+1|m)]$. The expressions of all Cartan-Weyl elements of $U_q[sl(n+1|m)]$ in terms of these Jacobson generators become very…
This paper concerns the construction of $su(r+1)$ Barut--Girardello coherent states in term of generalized Grassmann variables. We first introduce a generalized Weyl-Heisenberg algebra ${\cal A}(r)$ ($r \geq 1$) generated by $r$ pairs of…
A one-parameter generalized fermion algebra ${\cal B}_{\kappa}(1)$ is introduced. The Fock representation is studied. The associated coherent states are constructed and the polynomial representation, in the Bargmann sense, is derived. A…