Marko Stosic

TITLE: Parasupersymmetric Quantum Mechanics of Order 3 and a Generalized Witten Index

ABSTRACT: We give a generalization of Witten's supersymmetric quantum mechanics algebra ([1]) and Rubakov's and Spiridonov's second order parasupersymmetric algebra ([2]) to the case of order 3. We also generalized the notion of Witten's susy index to the parasupersymmetric cases and give one class of models satisfying our algebra. Finally, we showed the correspondence between the spectra of the Hamiltonian of the model and the index of the corresponding third order parasusy algebra.   

Main references:  

[1] Witten E.: Dynamical breaking of supersymmetry, Nucl. Phys. B185 (1981), 513-554 and Constraints on supersymmetry breaking, Nucl. PhysB202 (1982), 253-316. 

[2] Rubakov V.A. and Spiridonov V.P.: Parasupersymmetric quantum mechanics, Modern Physics Letters A3 (1988), 1337-1347. 

[3] Picken R.: An index from parasupersymmetry, preprint.

[4] Stosic, M. and Picken, R., Parasupersymmetric Quantum Mechanics of Order 3 and a Generalized Witten Index, math-ph/0407019.