Group theoretical foundations of fractional supersymmetry

@article{Azcrraga1995GroupTF,
  title={Group theoretical foundations of fractional supersymmetry},
  author={Jos{\'e} A. de Azc{\'a}rraga and Alan J. Macfarlane},
  journal={Journal of Mathematical Physics},
  year={1995},
  volume={37},
  pages={1115-1127}
}
Fractional supersymmetry denotes a generalization of supersymmetry which may be constructed using a single real generalized Grassmann variable, θ=θ,θn=0, for arbitrary integer n=2,3,.... An explicit formula is given in the case of general n for the transformations that leave the theory invariant, and it is shown that these transformations possess interesting group properties. It is shown also that the two generalized derivatives that enter the theory have a geometric interpretation as… 

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References

SHOWING 1-10 OF 65 REFERENCES

Extended fractional supersymmetric quantum mechanics

Recently, we presented a new class of quantum-mechanical Hamiltonians which can be written as the Fth power of a conserved charge: H=QF with F=2, 3,…. This construction, called fractional

Z3 ‐graded algebras and the cubic root of the supersymmetry translations

A generalization of supersymmetry is proposed based on Z3 ‐graded algebras. Introducing the objects whose ternary commutation relations contain the cubic roots of unity, e2πi/3, e4πi/3 and 1, the

A note on the meaning of covariant derivatives in supersymmetry

We analyze in this paper the group theoretical meaning of the covariant derivatives, and show that they are horizontal left‐invariant vector fields on superspace obtained from a (super)Lie group

The geometry of the one-dimensional supersymmetric non-linear sigma models

A new class of one-dimensional non-linear sigma models with N supersymmetries is constructed by generalising the action and the supersymmetry transformations of these theories. The study of the

Positive discrete series of osp(2‖2,R) and (para)supersymmetric quantum mechanics

The energy spectra of the systems corresponding to the superposition of (para) bosons and (para)fermions are analyzed. Such a study is subtended by the exploitation of the positive discrete series of

On q‐deformed supersymmetric classical mechanical models

Based on the idea of quantum groups and para‐Grassmannian variables, we present a generalization of supersymmetric classical mechanics with a deformation parameter q=exp(2πi/k) dealing with the k=3

A Generalized Method of Field Quantization

A method of field quantization is investigated which is more general than the usual methods of quantization in accordance with Bose of Fermi statistics, though these are included in the scheme. The
...