相关论文: A note on Gaussian integrals over paragrassmann va…

We construct path integral representations for the evolution operator of q-oscillators with root of unity values of q-parameter using Bargmann-Fock representations with commuting and non-commuting variables, the differential calculi being…

Some aspects of differential and integral calculi on generalized grassmann (paragrassmann) algebras are considered. The integration over paragrassmann variables is applied to evaluate the partition function for the $Z_{p+1}$ Potts model on…

Paragrassmann algebras with one and many paragrassmann variables are considered from the algebraic point of view without using the Green ansatz. Operators of differentiation with respect to paragrassmann variables and a covariant…

We describe coherent states and associated generalized Grassmann variables for a system of $m$ independent $q$-boson modes. A resolution of unity in terms of generalized Berezin integrals leads to generalized Grassmann symbolic calculus.…

Based on the idea of quantum groups and paragrassmann variables, we presenta generalization of supersymmetric classical mechanics with a deformation parameter $q= \exp{\frac{2 \pi i}{k}}$ dealing with the $k =3$ case. The coordinates of the…

The definitions of para-Grassmann variables and q-oscillator algebras are recalled. Some new properties are given. We then introduce appropriate coherent states as well as their dual states. This allows us to obtain a formula for the trace…

We review some aspects of the relation between ordinary coherent states and q-deformed generalized coherent states with some of the simplest cases of quantum Lie algebras. In particular, new properties of (q-)coherent states are utilized to…

Different analogs of quasiclassical limit for a q-oscillator which result in different (commutative and non-commutative) algebras of ``classical'' observables are derived. In particular, this gives the q-deformed Poisson brackets in terms…

Generalized $Z_k$-graded Grassmann variables are used to label coherent states related to the nilpotent representation of the q-oscillator of Biedenharn and Macfarlane when the deformation parameter is a root of unity. These states are then…

Extension of Feynman's path integral to quantum mechanics of noncommuting spatial coordinates is considered. The corresponding formalism for noncommutative classical dynamics related to quadratic Lagrangians (Hamiltonians) is formulated.…

This is a brief review of our recent work attempted at a generalization of the Grassmann algebra to the paragrassmann ones. The main aim is constructing an algebraic basis for representing `fractional' symmetries appearing in $2D$…

Using the Hecke $\hat R$-matrix, we give a definition of the lattice $(l,q)$-deformed $n$-component boson and Grassmann fields. Here $l$ is a deformation parameter for the commutation relations of "values" of these fields in two arbitrary…

A general deformation of the Heisenberg algebra is introduced with two deformed operators instead of just one. This is generalised to many variables, and permits the simultaneous existence of coherent states, and the transposition of…

Explicit general constructions of paragrassmann calculus with one and many variables are given. Relations of the paragrassmann calculus to quantum groups are outlined and possible physics applications are briefly discussed. This paper is…

In this paper, we propose a parametrised factor that enables inference on Gaussian networks where linear dependencies exist among the random variables. Our factor representation is effectively a generalisation of traditional Gaussian…

We define a generalized $(q;\alpha,\beta,\gamma;\nu)$-deformed oscillator algebra and study the number of its characteristics. We describe the structure function of deformation, analyze the classification of irreducible representations and…

We construct a family of random matrix models for the q-deformed Gaussian random variables G_\mu=a_\mu+a^\star_\mu where the annihilation operators a_\mu and creation operators a^\star_\nu fulfil the q-deformed commutation relation a_\mu…

As a first step towards a theory of differential equations involving para-Grassmann variables the linear equations with constant coefficients are discussed and solutions for equations of low order are given explicitly. A connection to…

For linear operators which factor with suitable assumptions concerning commutativity of the factors, we introduce several notions of a decomposition. When any of these hold then questions of null space and range are subordinated to the same…

The recently discovered general formulas for perturbative correlators in basic matrix models can be interpreted as the Schur-preservation property of Gaussian measures. Then substitution of Schur by, say, Macdonald polynomials, defines a…