Fractional Superspace Formulation of Generalized Super-Virasoro Algebras

Durand, Stéphane

doi:10.1142/s0217732392002275

Cited by 28 publications

(27 citation statements)

References 9 publications

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“…We shall rather focus our attention on some aspects of fractional SUSY and, more precisely, on fractional supersymmetric or parasupersymmetric (one-dimensional) nonrelativistic quantum mechanics, in the vein of the works in Refs. [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. From the point of view of quantum mechanics, a SUSY Hamiltonian comprises both bosonic and fermionic degrees of freedom.…”

Section: Generalities About Supersymmetrymentioning

confidence: 99%

On Fractional Supersymmetric Quantum Mechanics: The Fractional Supersymmetric Oscillator

Daoud¹,

Kibler²

2001

Symmetry and Structural Properties of Condensed Matter

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The Hamiltonian for a fractional supersymmetric oscillator is derived from three approaches. The first one is based on the Q-uon → boson + k-fermion decomposition. The second one starts from a generalized Weyl-Heisenberg algebra. Finally, the third one relies on the quantum algebra Uq(sl 2 ) where q is a root of unity. Generalities about supersymmetryWhat is supersymmetry ? Roughly speaking SUperSYmmetry or SUSY can be defined as a symmetry between bosons and fermions (as considered as elementary particles or simply as degrees of freedom). In other words, SUSY is based on the postulated existence of operators Q α which transform a bosonic field into a fermionic field and vice versa. In the context of quantum mechanics, such symmetry operators induce a Z 2 -grading of the Hilbert space of quantum states. In a more general way, fractional SUSY corresponds to a Z k -grading for which the Hilbert space involves both bosonic degrees of freedom (associated to bosons) and k-fermionic degrees of freedom (associated to k-fermions to be described below) with k ∈ N \ {0, 1} ; the case k = 2 corresponds to ordinary SUSY.Where does SUSY come from ? The concept of SUSY goes back to the sixtees when many attemps were done in order to unify external symmetries (described by the Poincaré group) and internal symmetries (described by gauge groups) for elementary particles. These attempts led to a no-go theorem by Coleman and Mandula 1 in 1967 which states that, under reasonable assumptions concerning the S-matrix, the unification of internal and external symmetries can be achieved solely through the introduction of the direct product of 1

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Section: Generalities About Supersymmetrymentioning

confidence: 99%

On Fractional Supersymmetric Quantum Mechanics: The Fractional Supersymmetric Oscillator

Daoud¹,

Kibler²

2001

Symmetry and Structural Properties of Condensed Matter

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“…, have been presented in the papers [7], [8]. It must be noted that the generators of the algebra (4.10) possess a general representation depending on an arbitrary 'para-conformal' weight ∆ (cf.…”

Section: Paraconformal Algebrasmentioning

confidence: 99%

“…[5] was based on a paragrassmann calculus defined in the frame of the Green representation for the paragrassmann algebra also known as the Green ansatz [6]. In a later paper [7] S. Durand is using the paragrassmann calculus developed 1 in Ref. [8] to derive interesting identities involving Virasoro-RNS -like generators.…”

Section: Introductionmentioning

confidence: 99%

Para-Grassmann Extensions of the Virasoro Algebra

Филиппов

Исаев

Kurdikov

1993

Int. J. Mod. Phys. A

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The paragrassmann differential calculus is briefly reviewed. Algebras of the transformations of the para-superplane preserving the form of the parasuperderivative are constructed and their geometric meaning is discussed. A new feature of these algebras is that they contain generators of the automorphisms of the paragrassmann algebra (in addition to Ramond-Neveu-Schwarz -like conformal generators). As a first step in analyzing these algebras we introduce more tractable multilinear algebras not including the new generators. In these algebras there exists a set of multilinear identities based on the cyclic polycommutators. Different possibilities of the closure are therefore admissible. The central extensions of the algebras are given. Their number varies from 1 to [ p+1 2 ] depending on the form of the closure chosen. Finally, simple explicit examples of the paraconformal transformations are given.

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“…Fractional supersymmetry (FSUSY) [9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28] is among the possible extensions of supersymmetry which have been studied in the literature. Basically, in such extensions, the generators of the Poincaré algebra are obtained as F −fold (F ∈ N ⋆ ) symmetric products of more fundamental generators.…”

Section: Introductionmentioning

confidence: 99%

Finite-dimensional Lie algebras of order F

Traubenberg

Slupinski

2002

Journal of Mathematical Physics

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F −Lie algebras are natural generalisations of Lie algebras (F = 1) and Lie superalgebras (F = 2). When F > 2 not many finite-dimensional examples are known. In this paper we construct finitedimensional F −Lie algebras F > 2 by an inductive process starting from Lie algebras and Lie superalgebras. Matrix realisations of F −Lie algebras constructed in this way from su(n), sp(2n) so(n) and sl(n|m), osp(2|m) are given. We obtain non-trivial extensions of the Poincaré algebra by Inönü-Wigner contraction of certain F −Lie algebras with F > 2.

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Fractional Superspace Formulation of Generalized Super-Virasoro Algebras

Cited by 28 publications

References 9 publications

On Fractional Supersymmetric Quantum Mechanics: The Fractional Supersymmetric Oscillator

On Fractional Supersymmetric Quantum Mechanics: The Fractional Supersymmetric Oscillator

Para-Grassmann Extensions of the Virasoro Algebra

Finite-dimensional Lie algebras of order F

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