N=4 Supersymmetric Quantum Mechanics with Magnetic Monopole

Abstract

We propose an N=4 supersymmetric quantum mechanics of a charged particle on a sphere in the background of Dirac magnetic monopole and study the system using the CP(1) model approach. We explicitly calculate the symmetry algebra taking the operator ordering ambiguity into consideration. We find that it is given by the superalgebra SU(1|2)x SU(2). We show that the Hamiltonian can be written in terms of the Casimir invariant of SU(2). Using this relation and the lower bound for angular momentm we obtain the energy spectrum. We then examine the ground energy sector to find that the N=4 supersymmetry is spontaneously broken to N=2 for certain values of the monopole charge.

7 pages

References in corpus (1)

• Supersymmetric Monopole Quantum Mechanics on Sphere

Cited by in corpus (8)

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• Isospin particle on $S^2$ with arbitrary number of supersymmetries
• Symmetries of deformed supersymmetric mechanics on Kähler manifolds
• N= 4 Supersymmetric Quantum Mechanical Model: Novel Symmetries
• BRST invariance and de Rham-type cohomology of 't Hooft-Polyakov monopole