18 research outputs found
Fsusy and Field Theoretical Construction
Following our previous work on fractional spin symmetries (FSS) \cite{6, 7},
we consider here the construction of field theoretical models that are
invariant under the supersymmetric algebra
Fractional Statistics in terms of the r-Generalized Fibonacci Sequences
We develop the basis of the two dimensional generalized quantum statistical
systems by using results on -generalized Fibonacci sequences. According to
the spin value of the 2d-quasiparticles, we distinguish four classes of
quantum statistical systems indexed by , ,
and . For quantum gases of quasiparticles
with , , we show that the statistical weights densities
are given by the integer hierarchies of Fibonacci sequences. This is a
remarkable result which envelopes naturally the Fermi and Bose statistics and
may be thought of as an alternative way to the Haldane interpolating
statistical method.Comment: Late
ON 1D FRACTIONAL SUPERSYMMETRIC THEORY
Following our previous work on fractional supersymmetry (FSUSY) [1,2], we focus here our contribute to the study of the superspace formulation in that is invariant under FSUSY where and defined by , we extend our formulation in the end of our paper to arbitrary with . Key-words Fractional superspace - Fractional Supersymmetry of order F - Fractional Supercharge - Covariant Derivativ
Finite-dimensional Lie algebras of order F
Lie algebras are natural generalisations of Lie algebras (F=1) and Lie
superalgebras (F=2). When not many finite-dimensional examples are known.
In this paper we construct finite-dimensional Lie algebras by an
inductive process starting from Lie algebras and Lie superalgebras. Matrix
realisations of Lie algebras constructed in this way from
and
, are given. We obtain non-trivial
extensions of the Poincar\'e algebra by In\"on\"u-Wigner contraction of certain
Lie algebras with .Comment: 20 pages, Late