Related papers: Fractional Supersymmetry as a Superposition of Ord…
This paper presents a new `partitional' approach to understanding or interpreting standard quantum mechanics (QM). The thesis is that the mathematics (not the physics) of QM is the Hilbert space version of the math of partitions on a set…
In this article, we propose new proportional fractional operators generated from local proportional derivatives of a function with respect to another function. We present some properties of these fractional operators which can be also…
The quantum mechanics of one degree of freedom exhibiting the exact conformal SL(2,R) symmetry is presented. The starting point is the classification of the unitary irreducible representations of the SL(2,R) group (or, to some extent, its…
This paper is a collection of lecture notes on the superfield approach in three- and four-dimensional supersymmetric quantum field theory. Many examples of the applications of this approach to different superfield models are considered.
We define a finite-dimensional partially formal supermanifold as a manifold having $q$ odd coordinates and $k + l$ even coordinates with $l$ of them taking only nilpotent values. We show that this notion can be used to formulate…
Fractional diffusion equations replace the integer-order derivatives in space and time by their fractional-order analogues. They are used in physics to model anomalous diffusion. This paper develops strong solutions of space-time fractional…
In the paper we begin a description of functional methods of quantum field theory for systems of interacting q-particles. These particles obey exotic statistics and are the q-generalization of the colored particles which appear in many…
Topological quantum matter exhibits a range of exotic phenomena when enriched by subdimensional symmetries. This includes new features beyond those that appear in the conventional setting of global symmetry enrichment. A recently discovered…
The $k$-symplectic structures appear in the geometric study of the partial differential equations of classical field theories. Meanwhile, we present a new application of the $k$-symplectic structures to investigate a type of systems of…
The hyperconfluent third-order supersymmetric quantum mechanics, in which all the factorization energies tend to a common value, is analyzed. It will be shown that the final potential as well can be achieved by applying consecutively a…
We study the supersymmetric quantum mechanical systems that arise from discrete light cone quantization of theories with minimal supersymmetry in various dimensions. These systems, which have previously arisen in the study of black hole…
We review the construction of minimally bosonized supersymmetric quantum mechanics and its relation to hidden supersymmetries in pure parabosonic (parafermionic) systems.
In this paper, we generalize fractional $q$-integrals by the method of $q$-difference equation. In addition, we deduce fractional Askey--Wilson integral, reversal type fractional Askey--Wilson integral and Ramanujan type fractional…
The fractional supersymmetry in the case of the non-relativistic motion of one anyon with fractional spin is realized. Thus the associated Hamiltonian is discussed.
We construct a class of quantum mechanical theories which are invariant under fermionic transformations similar to supersymmetry transformations. The generators of the transformations in this case, however, satisfy a BRST-like algebra.
We apply the supersymmetry approach to one-dimensional quantum systems with spatially-dependent mass, by including their ordering ambiguities dependence. In this way we extend the results recently reported in the literature. Furthermore, we…
We analyze general structure of N-fold supersymmetry which provides a systematic framework to construct weakly quasi-solvable quantum mechanical systems. Main ingredients of our analysis are dimensional analysis and introduction of an…
We apply the subordination principle to construct kinetic fractional statistical dynamics in the continuum in terms of solutions to Vlasov-type hierarchies. As a by-product we obtain the evolution of the density of particles in the…
A multi-parafermion basis of states for the Z_k parafermionic models is derived. Its generating function is constructed by elementary steps. It corresponds to the Andrews multiple-sum which enumerates partitions whose parts separated by the…
We relate the convergence of time-changed processes driven by fractional equations to the convergence of corresponding Dirichlet forms. The fractional equations we dealt with are obtained by considering a general fractional operator in…