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}
}
  • M. Plyushchay
  • Published 3 February 2004
  • Physics
  • Journal of Physics A
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. 
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11 Citations
Background Citations
1
Methods Citations
2

11 Citations

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References

SHOWING 1-10 OF 77 REFERENCES

NEW FEATURES IN SUPERSYMMETRY BREAKDOWN IN QUANTUM MECHANICS

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…

Supersymmetry without hermiticity within PT symmetric quantum mechanics

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

Nonlinear supersymmetry, quantum anomaly and quasi-exactly solvable systems

SECOND ORDER DERIVATIVE SUPERSYMMETRY, q DEFORMATIONS AND THE SCATTERING PROBLEM

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…

N-fold Supersymmetry in Quantum Mechanics - General Formalism -

The confluent algorithm in second-order supersymmetric quantum mechanics

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…

Superconformal quantum mechanics

Polynomial SUSY in quantum mechanics and second derivative Darboux transformations

Nonlinear supersymmetry in quantum mechanics: Algebraic properties and differential representation

...