# Nonlinear supersymmetry: From classical to quantum mechanics

@article{Plyushchay2004NonlinearSF, title={Nonlinear supersymmetry: From classical to quantum mechanics}, author={Mikhail S. Plyushchay}, journal={Journal of Physics A}, year={2004}, volume={37}, pages={10375-10384} }

Quantization of the nonlinear supersymmetry faces a problem of a quantum anomaly. For some classes of superpotentials, the integrals of motion admit corrections guaranteeing the preservation of the nonlinear supersymmetry at the quantum level. With an example of a system realizing the nonlinear superconformal symmetry, we discuss the nature of such corrections and speculate on their possible general origin.

## 11 Citations

### Supersymmetry Transformations for Delta Potentials

- Physics
- 2011

We make a detailed study of the first and second-order SUSY partners of a one- dimensional free Hamiltonian with a singular perturbation proportional to a Dirac delta function. It is shown that the…

### Nonlinear supersymmetry for spectral design in quantum mechanics

- Physics, Mathematics
- 2004

A nonlinear (polynomial, N-fold) SUSY approach to preparation of quantum systems with pre-planned spectral properties is reviewed. The full classification of ladder-reducible and irreducible chains…

### Coherent states for Hamiltonians generated by supersymmetry

- Physics
- 2007

Coherent states are derived for one-dimensional systems generated by supersymmetry from an initial Hamiltonian with a purely discrete spectrum for which the levels depend analytically on their…

### Nonlinear supersymmetric quantum mechanics: concepts and realizations

- Mathematics
- 2012

The nonlinear supersymmetric (SUSY) approach to spectral problems in quantum mechanics (QM) is reviewed. Its building from the chains (ladders) of linear SUSY systems is outlined and different…

### Trends in Supersymmetric Quantum Mechanics

- PhysicsIntegrability, Supersymmetry and Coherent States
- 2019

Along the years, supersymmetric quantum mechanics (SUSY QM) has been used for studying solvable quantum potentials. It is the simplest method to build Hamiltonians with prescribed spectra in the…

### Coherent states for SUSY partner Hamiltonians

- Physics
- 2008

Coherent states are constructed for systems generated by supersymmetry from an initial Hamiltonian with a purely discrete spectrum such that the levels depend analytically on their subindex. The…

### Rosen–Morse Potential and Its Supersymmetric Partners

- Physics
- 2011

A set of supersymmetric partners of the Rosen–Morse potential is generated. The corresponding physical properties are studied—in particular, the change in intensity of the singularities at the…

### Three dimensional N=4 supersymmetric mechanics with Wu-Yang monopole

- Physics
- 2010

We propose Lagrangian and Hamiltonian formulations of a N=4 supersymmetric three-dimensional isospin-carrying particle moving in the non-Abelian field of a Wu-Yang monopole and in some specific…

### Supersymmetric partners of the trigonometric Pöschl–Teller potentials

- Physics
- 2008

The first- and second-order supersymmetry transformations are used to generate Hamiltonians with known spectra departing from the trigonometric Pöschl–Teller potentials. The several possibilities of…

## References

SHOWING 1-10 OF 77 REFERENCES

### NEW FEATURES IN SUPERSYMMETRY BREAKDOWN IN QUANTUM MECHANICS

- Physics
- 1996

The supersymmetric quantum mechanical model based on higher-derivative supercharge operators possessing unbroken supersymmetry and discrete energies below the vacuum state energy is described. As an…

### New possibilities for supersymmetry breakdown in quantum mechanics and second-order irreducible Darboux transformations

- Physics, Mathematics
- 1999

### SECOND ORDER DERIVATIVE SUPERSYMMETRY, q DEFORMATIONS AND THE SCATTERING PROBLEM

- Mathematics, Physics
- 1995

In a search for pairs of quantum systems linked by dynamical symmetries, we give a systematic analysis of novel extensions of standard one-dimensional supersymmetric quantum mechanics. The most…

### The confluent algorithm in second-order supersymmetric quantum mechanics

- Physics
- 2003

The confluent algorithm, a degenerate case of the second-order supersymmetric quantum mechanics, is studied. It is shown that the transformation function must asymptotically vanish to induce…

### Polynomial SUSY in quantum mechanics and second derivative Darboux transformations

- Mathematics, Physics
- 1994