Conformal Parasupersymmetry in Quantum Mechanics

Abstract

Conformal parasupersymmetry of order 2 is exemplified using a one-dimensional quantum mechanical system. Symmetry generators are seen to realize trilinear structure relations. The relevant representations of this novel symmetry algebra are constructed and shown to allow for a complete determination of the energy spectrum and wave functions of the system.

Factorization: little or great algorithm?

“…The idea was proposed by Rubakov and Spiridonov [110], who designed the supercharges Q ± in the form of nilpotent matrices with bosonic entries. Alternative models were soon proposed by Beckers and Debergh (an exact parasupersymmetry, triple degeneracy [111,112], a parasuperspace [113]) and by Durand and Vinet (cyclotronic and Morse models [114], the spin 1 representation of a ± [115]); another interesting approach is due to Plyushchay [116,117]. It is also worth noting that the fundamental subject of anyons (see Goldin et al and Wilczek [118][119][120]) admits as well a natural algebraic treatment [121,122].…”

Two-dimensional fractional supersymmetric conformal and logarithmic conformal field theories and two point functions

“…where {...} per , means, the sum of products of all possible permutations of generators G r k . This algebra has nontrivial central extensions, it is shown [16,46] that there is only one subalgebra (containing G r 's as well as L n 's), the central extension for which is trivial. This algebra is the one generated by [L −1 , L 0 , G −1/(F +1) ] and their antiholomorphic counterparts…”

Two-Dimensional Fractional Supersymmetric Conformal Field Theories and the Two-Point Functions

“…It is shown [16,25] that there is only one subalgera (containing G-generators as well as L n 's), the central extension for which is trivial. This algebra is the one generated by {L −1 , L 0 , G −1/3 }.…”

“…This algebra, which contains the Virasoro algebra (18) as a subalgebra, has nontrivial central extensions. It is shown [16,25] that there is only one subalgera (containing G-generators as well as L n 's), the central extension for which is trivial. This algebra is the one generated by {L −1 , L 0 , G −1/3 }.…”