Supersymmetry breaking in noncommutative quantum mechanics
J Ben Geloun, F G Scholtz
TL;DR
This paper investigates how noncommutativity in a two-dimensional quantum plane affects supersymmetry, revealing partial breaking of supersymmetry and linking it to time reversal symmetry breaking.
Contribution
It introduces a formulation of supersymmetric quantum mechanics on a noncommutative plane and analyzes supersymmetry breaking effects in this setting.
Findings
Supersymmetry is partially broken in noncommutative space.
Only half of the supercharges are conserved.
Breaking of supersymmetry is related to time reversal symmetry breaking.
Abstract
Supersymmetric quantum mechanics is formulated on a two dimensional noncommutative plane and applied to the supersymmetric harmonic oscillator. We find that the ordinary commutative supersymmetry is partially broken and only half of the number of supercharges are conserved. It is argued that this breaking is closely related to the breaking of time reversal symmetry arising from noncommutativity.
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