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… 
View PDF on arXiv
60 Citations
Highly Influential Citations
1
Background Citations
3
Methods Citations
4

60 Citations

Fractional supersymmetry and Fth-roots of representations

A generalization of super-Lie algebras is presented. It is then shown that all known examples of fractional supersymmetry can be understood in this formulation. However, the incorporation of…

Local Fractional Supersymmetry for Alternative Statistics

A group theory justification of one-dimensional fractional supersymmetry is proposed using an analog of a coset space, just like the one introduced in 1-D supersymmetry. This theory is then gauged to…

2D fractional supersymmetry and conformal field theory for alternative statistics

Fractional Supersymmetry and F − fold Lie

It is generally held that supersymmetry is the only non-trivial extension of the Poincaré algebra. This point of view is based on the two theorems [1, 2]. However, as usual, if some of the…

Field Theoretic Realizations for Cubic Supersymmetry

We consider a four-dimensional space–time symmetry which is a nontrivial extension of the Poincare algebra, different from supersymmetry and not contradicting a priori the well-known no-go theorems.…

Nontrivial Extensions of the 3D-Poincaré Algebra and Fractional Supersymmetry for Anyons

Nontrivial extensions of three-dimensional Poincare algebra, beyond the supersymmetric one, are explicitly constructed. These algebraic structures are the natural three-dimensional generalizations of…

NON-ABELIAN FRACTIONAL SUPERSYMMETRY IN TWO DIMENSIONS

Non-Abelian fractional supersymmetry algebra in two dimensions is introduced utilizing Uq(sl(2,ℝ)) at roots of unity. Its representations and the matrix elements are obtained. The dual of it is…

Fractional supersymmetry and hierarchy of shape invariant potentials

Fractional supersymmetric quantum mechanics is developed from a generalized Weyl-Heisenberg algebra. The Hamiltonian and the supercharges of fractional supersymmetric dynamical systems are built in…

Quantum mechanical symmetries and topological invariants

Fractional Super-Multi-Virasoro Algebra

An n-dimensional fractional supersymmetry theory is algebraically constructedon the n-dimensional multicomplex space Mn. By emphasizing its appearanceas a special case of generalized Clifford algebra…
...

References

SHOWING 1-10 OF 65 REFERENCES

Fractional supersymmetry and quantum mechanics

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…

N = 12 supersymmetry in two dimensions

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…

Fractional Supersymmetries in Perturbed Coset Cfts and Integrable Soliton Theory

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…
...