Superpotential for Novel Symmetry in Real and Complex Space

We propose a new “superpotential” and find that neither the supersymmetric energy conditions nor the associated shape invariance conditions remain valid. On the other hand, a new energy condition En+−En(−)=2λ between the two partner Hamiltonians H(±) emerges. A mathematical proof supports the presen...

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Bibliographic Details
Published in:Symmetry (Basel) 2022-12, Vol.14 (12), p.2632
Main Author: Rath, Biswanath
Format: Article
Language:English
Subjects:
Eigenvalues
Energy
invalidity
Invariance
novel symmetry
Phase transitions
real and complex space
shape-invariance
supersymmetry
Symmetry
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Summary:We propose a new “superpotential” and find that neither the supersymmetric energy conditions nor the associated shape invariance conditions remain valid. On the other hand, a new energy condition En+−En(−)=2λ between the two partner Hamiltonians H(±) emerges. A mathematical proof supports the present findings, with examples being presented. It is observed that when the superpotential is associated with discontinuity or distortion, the SUSY energy conditions and the shape invariance conditions will no longer hold well. The above formalism is also valid in complex space for models involving PT-symmetry.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym14122632