$2D-$ Fractional Supersymmetry and Conformal Field Theory for alternative statistics

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dc.creatorde Traubenberg, M. Rausch
dc.creatorSimon, P.
dc.date1996-06-28
dc.date1998-01-30
dc.date.accessioned2026-07-07T09:04:23Z
dc.date.available2026-07-07T09:04:23Z
dc.descriptionSupersymmetry can be consistently generalized in one and two dimensional spaces, fractional supersymmetry being one of the possible extension. 2D fractional supersymmetry of arbitrary order $F$ is explicitly constructed using an adapted superspace formalism. This symmetry connects the fractional spin states ($0,{1 \over F}, ...,{F-1 \over F}$). Besides the stress momentum tensor, we obtain a conserved current of spin($1 + {1 \over F})$. The coherence of the theory imposes strong constraints upon the commutation relations of the modes of the fields. The creation and annihilation operators turn out to generate alternative statistics, currently referred as quons in the literature. We consider, with a special attention, the consistence of the algebra, on the level of the Hilbert space and the Green functions. The central charges are generally irrational numbers except for the particular cases $F=2,3,4$. A natural classification emerges according to the decomposition of $F$ into its product of prime numbers leading to sub-systems with smaller symmetries.
dc.description24 pages, LaTex, the algebraic structure is given with more details, a special attention is paid on the level of the associativity, references have been added, one author has been suppressed, Title and abstract has been modified, to appear in Nucl. Phys. B
dc.identifierhttps://arxiv.org/abs/hep-th/9606188
dc.identifierhttp://arxiv.org/abs/hep-th/9606188
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/149360
dc.subjectHigh Energy Physics - Theory
dc.title$2D-$ Fractional Supersymmetry and Conformal Field Theory for alternative statistics
dc.typetext

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