Non-Abelian monopole in the parameter space of point-like interactions

Abstract

h i g h l i g h t s• Supersymmetric quantum mechanics is an ideal playground for studying geometric phase.• We determine the parameter space of supersymmetric point-like interactions. • Berry's connection is given by a Wu-Yang-like magnetic monopole in SU(2) Yang-Mills. a b s t r a c tWe study non-Abelian geometric phase in N = 2 supersymmetric quantum mechanics for a free particle on a circle with two pointlike 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.

Effects of two successive parity-invariant point interactions on one-dimensional quantum transmission: Resonance conditions for the parameter space

“…It has been known that the parameter space in one dimension is characterized by U (2), while those in two dimensions and three dimensions are characterized by U (1). Several authors [27,28,29,30,31,32,33,34,35,36,37] reported that the interesting characteristics of supersymmetry, geometric phase, anholonomy, duality, and so on appear owing to the large parameter space for the junction conditions in one dimension. These previous works placed a special emphasis relatively on bound states in one-dimensional systems.…”

Extended supersymmetry with central charges in Dirac action with curved extra dimensions

“…, · · · also satisfy the imposed boundary condition for the mode functions f (n) α . 7 Although we can also define the supercharges with the replacement of the operators with the Roman and the Greek letters, those are essentially same as the ones given in the above. Therefore, we can consider that the central charges in this SUSY algebra result from the symmetries in the extra dimensions.…”

“…Furthermore, we examine the model of the S 2 extra dimension with a magnetic monopole background and confirm that the N-extended QM SUSY explains the degeneracy of the 4D mass spectrum.So far, quantum-mechanical supersymmetry (QM SUSY) has attracted much attention and been applied to the various research areas, e.g. exactly solvable quantum mechanics [1][2][3][4][5], Berry phase [6][7][8], black holes and AdS/CFT [9-13], Sachdev-Ye-Kitaev model [14][15][16][17][18], extra dimensional models [19][20][21][22][23][24] and so on.It's extensions are also investigated. The N-extended supersymmetry is the extension which includes N independent supercharges in the supersymmetry algebra [25][26][27][28][29][30][31][32].…”

Extended supersymmetry with central charges in higher dimensional Dirac action

“…These days, the QM SUSY is applied to a wide range of research areas, e.g. exactly solvable systems in quantum mechanics [2][3][4][5][6], Berry phase [7][8][9], black holes and AdS/CFT [10][11][12][13][14], Sachdev-Ye-Kitaev model [15][16][17][18][19], extra dimensional models [20][21][22][23][24][25] and so on. Recent trends in QM SUSY are reviewed in Ref.…”