Non-Abelian Monopole in the Parameter Space of Point-like Interactions

Abstract

We study non-Abelian geometric phase in $\mathcal{N}=2$ supersymmetric quantum mechanics for a free particle on a circle with two point-like interactions at antipodal points. We show that non-Abelian Berry's connection is that of $SU(2)$ magnetic monopole discovered by Moody, Shapere and Wilczek in the context of adiabatic decoupling limit of diatomic molecule.

15 pages, 3 tikz figures; minor corrections

References in corpus (5)

• An angular momentum approach to quadratic Fourier transform, Hadamard matrices, Gauss sums, mutually unbiased bases, unitary group and Pauli group
• The Geometric Phase in Supersymmetric Quantum Mechanics
• Non-Abelian Berry Phases and BPS Monopoles
• Rotor Spectra, Berry Phases, and Monopole Fields: from Antiferromagnets to QCD
• Parasupersymmetry in Quantum Graphs

Cited by in corpus (4)

• Resonant Transmission in One-Dimensional Quantum Mechanics with Two Independent Point Interactions: Full Parameter Analysis
• Bloch vector, disclination and exotic quantum holonomy
• Instantons and Berry's connections on quantum graph
• Correspondence of topological classification between quantum graph extra dimension and topological matter