# Schwarzian derivative treatment of the quantum second-order supersymmetry anomaly, and coupling-constant metamorphosis

## Abstract

A canonical quantization scheme applied to a classical supersymmetric system with quadratic in momentum supercharges gives rise to a quantum anomaly problem described by a specific term to be quadratic in Planck constant. We reveal a close relationship between the anomaly and the Schwarzian derivative, and specify a quantization prescription which generates the anomaly-free supersymmetric quantum system with second order supercharges. We also discuss the phenomenon of a coupling-constant metamorphosis that associates quantum systems with the first-order supersymmetry to the systems with the second-order supercharges.

- Authors:

- Publication Date:

- OSTI Identifier:
- 22617468

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Annals of Physics; Journal Volume: 377; Other Information: Copyright (c) 2016 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; COUPLING CONSTANTS; NONLINEAR PROBLEMS; QUANTIZATION; QUANTUM SYSTEMS; SUPERSYMMETRY

### Citation Formats

```
Plyushchay, Mikhail S., E-mail: mikhail.plyushchay@usach.cl.
```*Schwarzian derivative treatment of the quantum second-order supersymmetry anomaly, and coupling-constant metamorphosis*. United States: N. p., 2017.
Web. doi:10.1016/J.AOP.2016.12.003.

```
Plyushchay, Mikhail S., E-mail: mikhail.plyushchay@usach.cl.
```*Schwarzian derivative treatment of the quantum second-order supersymmetry anomaly, and coupling-constant metamorphosis*. United States. doi:10.1016/J.AOP.2016.12.003.

```
Plyushchay, Mikhail S., E-mail: mikhail.plyushchay@usach.cl. Wed .
"Schwarzian derivative treatment of the quantum second-order supersymmetry anomaly, and coupling-constant metamorphosis". United States.
doi:10.1016/J.AOP.2016.12.003.
```

```
@article{osti_22617468,
```

title = {Schwarzian derivative treatment of the quantum second-order supersymmetry anomaly, and coupling-constant metamorphosis},

author = {Plyushchay, Mikhail S., E-mail: mikhail.plyushchay@usach.cl},

abstractNote = {A canonical quantization scheme applied to a classical supersymmetric system with quadratic in momentum supercharges gives rise to a quantum anomaly problem described by a specific term to be quadratic in Planck constant. We reveal a close relationship between the anomaly and the Schwarzian derivative, and specify a quantization prescription which generates the anomaly-free supersymmetric quantum system with second order supercharges. We also discuss the phenomenon of a coupling-constant metamorphosis that associates quantum systems with the first-order supersymmetry to the systems with the second-order supercharges.},

doi = {10.1016/J.AOP.2016.12.003},

journal = {Annals of Physics},

number = ,

volume = 377,

place = {United States},

year = {Wed Feb 15 00:00:00 EST 2017},

month = {Wed Feb 15 00:00:00 EST 2017}

}

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