Related papers: Vector Supersymmetry from OSp(3,2|2): Casimir Oper…
We find the GKO coset construction of the dimension 4 Casimir operator that contains the quartic WZW currents contracted with completely symmetric SU(N) invariant tensors of ranks 4, 3, and 2. The requirements, that the operator product…
Higher dimensional supersymmetric quantum mechanics is studied. General properties of the two dimensional case are presented. For three spatial dimesions or higher, a spin structure is shown to arise naturally from the nonrelativistic…
We explicitly constructed the generators of $SU(n+1)$ group which commute with the supercharges of N=4 supersymmetric $\mathbb{CP}^n$ mechanics in the background U(n) gauge fields. The corresponding Hamiltonian can be represented as a…
The new method based on the SUSY algebra with supercharges of higher order in derivatives is proposed to search for dynamical symmetry operators in 2-dim quantum and classical systems. These symmetry operators arise when closing the SUSY…
This study reconsidered the N=1 supersymmetric extension of the W_3 algebra which was studied previously. This extension consists of seven higher spin supercurrents (fourteen higher spin currents in the components) as well as the N=1 stress…
Two known 2-dim SUSY quantum mechanical constructions - the direct generalization of SUSY with first-order supercharges and Higher order SUSY with second order supercharges - are combined for a class of 2-dim quantum models, which {\it are…
We show that the so-called semi-simple extended Poincar\'{e} (SSEP) algebra in $D$ dimensions can be obtained from the anti-de~Sitter algebra $\mathfrak{so} \left( D-1,2 \right)$ by means of the $S$-expansion procedure with an appropriate…
A bosonic operator of U_q(osp(1|2)) that anticommutes with the fermionic generators appears to be useful to describe the relations in the centre of U_q(osp(1|2)) for q a root of unity (in the unrestricted specialisation). As in the…
In this paper, we discuss the In\"on\"u-Winger contraction of the conformal algebra. We start with the light-cone form of the Poincar\'e algebra and extend it to write down the conformal algebra in $d$ dimensions. To contract the conformal…
A new superconformal mechanics with OSp(4|2) symmetry is obtained by gauging the U(1) isometry of a superfield model. It is the one-particle case of the new N=4 super Calogero model recently proposed in arXiv:0812.4276 [hep-th]. Classical…
We present the general ideas on SuperSymmetric Quantum Mechanics (SUSY-QM) using different representations for the operators in question, which are defined by the corresponding bosonic Hamiltonian as part of SUSY Hamiltonian and its…
We present an alternative method of exploring the component structure of an integer super-helicity Y=s (for any integers) irreducible representation of the Super-Poincare group. We use it to derive the component action and the SUSY…
The algebra su(2) is derived from two commuting quon algebras for which the parameter q is a root of unity. This leads to a polar decomposition of the shift operators of the group SU(2). The Wigner-Racah algebra of SU(2) is developed in a…
We study theories of 4D, N=1 supersymmetric massless, arbitrary integer superspins. A new state-of-the art is being established by the discovery of a new series of such theories for arbitrary superspin Y (Y=s for any integer s) The lowest…
In this paper, we survey the nature of spinors and supersymmetry (SUSY) in various types of spaces. We treat two distinct types of spaces: flat spaces and spaces of constant (non-zero) curvature. The flat spaces we consider are either three…
In the relation between the linear (L) supersymmetry (SUSY) representation and the nonlinear (NL) SUSY representation we discuss the role of the Wess-Zumino gauge. We show in two dimensional spacetime that a spontaneously broken LSUSY…
This paper is the second paper in a series of four papers that introduce cybersusy, which is a new method for analyzing supersymmetry breaking in the standard supersymmetric model (SSM). The first paper was a summary of the results and the…
We construct a novel higher-spin theory of gravity in 2+1 spacetime dimensions. The construction is based on a higher-spin super-algebra extending the Poincare group. Our algebra accommodates all integer and half-integer spins from 1 to…
Supersymmetrical (SUSY) intertwining relations are generalized to the case of quantum Hamiltonians in Minkowski space. For intertwining operators (supercharges) of second order in derivatives the intertwined Hamiltonians correspond to…
Using recent results on string on $AdS_{3}\times N^d$, where N is a d-dimensional compact manifold, we re-examine the derivation of the non trivial extension of the (1+2) dimensional-Poincar\'e algebra obtained by Rausch de Traubenberg and…