Twist Deformations of the Supersymmetric Quantum Mechanics

TL;DR

This paper explores how abelian twist deformations can be applied to N-extended supersymmetric quantum mechanics, preserving its algebraic structure and leading to twisted operators with modified (anti)commutation relations.

Contribution

It introduces two methods for implementing abelian twists in supersymmetric quantum mechanics and analyzes their effects on the algebraic structure and operator relations.

Findings

Deformation preserves super-Hopf algebra structure.

Twisted operators satisfy modified (anti)commutators.

Differences between fermionic and bosonic twist implementations are discussed.

Abstract

The N-extended Supersymmetric Quantum Mechanics is deformed via an abelian twist which preserves the super-Hopf algebra structure of its Universal Enveloping Superalgebra. Two constructions are possible. For even N one can identify the 1D N-extended superalgebra with the fermionic Heisenberg algebra. Alternatively, supersymmetry generators can be realized as operators belonging to the Universal Enveloping Superalgebra of one bosonic and several fermionic oscillators. The deformed system is described in terms of twisted operators satisfying twist-deformed (anti)commutators. The main differences between an abelian twist defined in terms of fermionic operators and an abelian twist defined in terms of bosonic operators are discussed.