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

## Abstract

We study non-Abelian geometric phase in 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. - Highlights: • 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.

- Authors:

- Publication Date:

- OSTI Identifier:
- 22403506

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Annals of Physics (New York); Journal Volume: 351; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; DECOUPLING; GEOMETRY; INTERACTIONS; MOLECULES; QUANTUM MECHANICS; SU-2 GROUPS; SUPERSYMMETRY; YANG-MILLS THEORY

### Citation Formats

```
Ohya, Satoshi, E-mail: ohyasato@fjfi.cvut.cz.
```*Non-Abelian monopole in the parameter space of point-like interactions*. United States: N. p., 2014.
Web. doi:10.1016/J.AOP.2014.10.013.

```
Ohya, Satoshi, E-mail: ohyasato@fjfi.cvut.cz.
```*Non-Abelian monopole in the parameter space of point-like interactions*. United States. doi:10.1016/J.AOP.2014.10.013.

```
Ohya, Satoshi, E-mail: ohyasato@fjfi.cvut.cz. Mon .
"Non-Abelian monopole in the parameter space of point-like interactions". United States. doi:10.1016/J.AOP.2014.10.013.
```

```
@article{osti_22403506,
```

title = {Non-Abelian monopole in the parameter space of point-like interactions},

author = {Ohya, Satoshi, E-mail: ohyasato@fjfi.cvut.cz},

abstractNote = {We study non-Abelian geometric phase in 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. - Highlights: • 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.},

doi = {10.1016/J.AOP.2014.10.013},

journal = {Annals of Physics (New York)},

number = ,

volume = 351,

place = {United States},

year = {Mon Dec 15 00:00:00 EST 2014},

month = {Mon Dec 15 00:00:00 EST 2014}

}

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