Related papers: Invariants in Supersymmetric Classical Mechanics
In this paper we classify M\"{o}bius invariant differential operators of second order in two dimensional Euclidean space, and establish a Liouville type theorem for general M\"{o}bius invariant elliptic equations.
It is argued that the noncommutativity approach to fully supersymmetric field theories on the lattice suffers from an inconsistency. Supersymmetric quantum mechanics is worked out in this formalism and the inconsistency is shown both in…
Motivated by the shape invariance condition in supersymmetric quantum mechanics, we develop an algebraic framework for shape invariant Hamiltonians with a general change of parameters. This approach involves nonlinear generalizations of Lie…
We investigate hidden symmetries of P,T-invariant system of topologically massive U(1) gauge fields. For this purpose, we propose a pseudoclassical model giving rise to this field system at the quantum level. The model contains a parameter,…
It is shown that the method of the nonlinear realization of local supersymmetry previously developed in framework of supergravity being applied to the n=(2,2) superconformal symmetry allows one to get the new form of the exactly solvable…
Bosonic quantum conversion systems can be modeled by many-particle single-mode Hamiltonians describing a conversion of $n$ molecules of type A into $m$ molecules of type B and vice versa. These Hamiltonians are analyzed in terms of…
We study new Legendre transforms in classical mechanics and investigate some of their general properties. The behaviour of the new functions is analyzed under coordinate transformations.When invariance under different kinds of…
A supersymmetric approach to string quantum cosmology based on the non-compact, global duality symmetries of the effective action is developed. An N=2 supersymmetric action is derived whose bosonic component is the…
We show that the single-mode parafermionic type systems possess supersymmetry, which is based on the symmetry of characteristic functions of the parafermions related to the generalized deformed oscillator of Daskaloyannis et al. The…
Motivated by the duality of normalizable states and the presence of the quasi-parity quantum number q=+/-1 in PT symmetric (non-Hermitian) quantum mechanical potential models, the relation of PT symmetry and supersymmetry (SUSY) is studied.…
It is shown that a symmetric massless bosonic higher-spin field can be described by a traceless tensor field with reduced (transverse) gauge invariance. The Hamiltonian analysis of the transverse gauge invariant higher-spin models is used…
In this study we work on a novel Hamiltonian system which is Liouville integrable. In the integrable Hamiltonian model, conserved currents can be represented as Binomial polynomials in which each order corresponds to the integral of motion…
We derive bosonic-type formulas for the characters of $\hat{sl_2}$ coinvariants.
We give the generalization of a recent variational formulation for nonconservative classical mechanics, for fermionic and sypersymmetric systems. Both cases require slightly modified boundary conditions. The supersymmetric version is given…
Two complementary approaches of N = 2 fractional supersymmetric quantum mechanics of order k are studied in this article. The first one, based on a generalized Weyl-Heisenberg algebra W(k) (that comprizes the affine quantum algebra…
We investigate a one dimensional quantum mechanical model, which is invariant under translations and dilations but does not respect the conventional conformal invariance. We describe the possibility of modifying the conventional conformal…
Lorentzian manifolds with vanishing second covariant derivative of the Riemann tensor are studied. Their existence, classification and explicit local expression are considered. Related issues and open questions are briefly commented.
Similarly to the ordinary bosonic Liouville field theory, in its N=1 supersymmetric version an infinite set of operator valued relations, the ``higher equations of motions'', holds. Equations are in one to one correspondence with the…
This paper is devoted to the construction of differential geometric invariants for the classification of "Quaternionic" vector bundles. Provided that the base space is a smooth manifold of dimension two or three endowed with an involution…
We study the gauge invariant cosmological perturbations up to second order. We show that there are infinite families of gauge invariant variables at both of the first and second orders. The conversion formulae among different families are…