Extended Fractional Supersymmetric Quantum Mechanics

Abstract

Recently, we presented a new class of quantum-mechanical Hamiltonians which can be written as the F th power of a conserved charge: H = Q F with F = 2, 3, ... . This construction, called fractional supersymmetric quantum mechanics, was realized in terms of a paragrassmann variable θ of order F , which satisfies θ F = 0. Here, we present an alternative realization of such an algebra in which the internal space of the Hamiltonians is described by a tensor product of two paragrassmann variables of orders F and F − 1 respectively. In particular, we find q-deformed relations (where q are roots of unity) between different conserved charges. *

Fractional Superspace Formulation of Generalized Mechanics

“…Our previous results (12) and (27) are recovered for F = 2 and F = 3, with the notation ψ (1) ≡ ψ and ψ (2) ≡ φ. For F = 1, we simply have δx = ǫẋ.…”

Poincaré and sl(2) algebras of order 3

“…In [26], an Inönü-Wigner contraction was done 5) and the limit ε → 0 realised the contraction. The contracted Lie algebra of order 3 is given by…”

Extension of the Poincaré Symmetry and Its Field Theoretical Implementation

“…Spiridonov in [12]. Furthermore, fractional supersymmetry was also analysed as a quantum mechanics model by a series of authors in [13,14,15,16,17,18,19,20]. Let us recall that a different approach was given by R. Kerner in [21].…”