Stochastic quantization is applied to derivation of the equations for the Wilson loops and generating functionals of the Wilson loops in the large-N limit. These equations are treated both in the coordinate and momentum representations. In the first case the connection of the suggested approach with the problem of random closed contours and supersymmetric quantum mechanics is established, and t...

I present ongoing developments on hybrid models which combine the potential model, for the description of the background, with the R-matrix model, for the description of discrete states. Physical parameters of discrete states are converted into formal R-matrix parameters, taking into account the potential background. The nuclear part of this potential is constructed by a new variant of an inver...

A way to construct and classify the three dimensional polynomially deformed algebras is given and the irreducible representations is presented. for the quadratic algebras 4 different algebras are obtained and for cubic algebras 12 different classes are constructed. Applications to quantum mechanical systems including supersymmetric quantum mechanics are discussed

We first obtain by analogy with the continuous (differential) case the general solution of a discrete Riccati equation. Our results can be considered the discrete analog of Miel-nik's construction in supersymmetric quantum mechanics [J. Moreover, we establish the full equivalence of our discrete Riccati equation and a corresponding homogeneous second order discrete linear equation. We present a...

The minimal bosonization of supersymmetry in terms of one bosonic degree of freedom is considered. A nontrivial relationship of the construction to the Witten supersymmetric quantum mechanics is illustrated with the help of the simplest N = 2 SUSY system realized on the basis of the ordinary (undeformed) bosonic oscillator. It is shown that the generalization of such a construction to the case ...

We study supersymmetric quantum mechanics on RP n , SO(n), G 2 and U(2) to examine Witten's Morse theory concretely. We confirm the simple instanton picture of the de Rham cohomology that has been given in a previous paper. We use a reflection symmetry of each theory to select the true vacuums. The number of selected vacuums agrees with the de Rham cohomology for each of the above man-ifolds.

The class of relativistic spin particle models reveals the ‘quantization’ of parameters already at the classical level. The special parameter values emerge if one requires the maximality of classical global continuous symmetries. The same requirement applied to a non-relativistic particle with odd degrees of freedom gives rise to supersymmetric quantum mechanics. Coupling classical non-relativi...

Using supersymmetric quantum mechanics we construct the quasiexactly solvable (QES) potentials with arbitrary two known eigenstates. The QES potential and the wave functions of the two energy levels are expressed by some generating function the properties of which determine the state numbers of these levels. Choosing different generating functions we present a few explicit examples of the QES p...

It is argued that the low-energy dynamics of k monopoles in N=2 supersymmetric Yang-Mills theory are determined by an N=4 supersymmetric quantum mechanics based on the moduli space of k static monople solutions. This generalises Manton’s “geodesic approximation” for studying the low-energy dynamics of (bosonic) BPS monopoles. We discuss some aspects of the quantisation and in particular argue t...

Two complementary approaches ofN = 2 fractional supersymmetric quantum mechanics of order k are studied in this article. The first one, based on a generalized Weyl-Heisenberg algebra Wk (that comprizes the affine quantum algebra Uq(sl2) with q k = 1 as a special case), apparently contains solely one bosonic degree of freedom. The second one uses generalized bosonic and kfermionic degrees of fre...