# ${\mathcal N}$-FOLD SUPERSYMMETRIC QUANTUM MECHANICS WITH REFLECTIONS

@article{Tanaka2011mathcalNS, title={\$\{\mathcal N\}\$-FOLD SUPERSYMMETRIC QUANTUM MECHANICS WITH REFLECTIONS}, author={Toshiaki Tanaka}, journal={International Journal of Modern Physics A}, year={2011}, volume={27}, pages={1250102} }

We formulate -fold supersymmetry in quantum mechanical systems with reflection operators. As in the cases of other systems, they possess the two significant characters of -fold supersymmetry, namely, almost isospectrality and weak quasi-solvability. We construct explicitly the most general one- and two-fold supersymmetric quantum mechanical systems with reflections. In the case of , we find that there are seven inequivalent such systems, three of which are characterized by three arbitrary…

## 6 Citations

### The Hahn superalgebra and supersymmetric Dunkl oscillator models

- Mathematics
- 2013

A supersymmetric extension of the Hahn algebra is introduced. This quadratic superalgebra, which we call the Hahn superalgebra, is constructed using the realization provided by the Dunkl oscillator…

### Graded Geometric Structures Underlying F-Theory Related Defect Theories

- Mathematics
- 2013

In the context of F-theory, we study the related eight-dimensional super-Yang–Mills theory and reveal the underlying supersymmetric quantum mechanics algebra that the fermionic fields localized on…

### Two-step shape invariance in the framework of $$\mathcal{N}$$-fold supersymmetry

- Mathematics, Physics
- 2015

We extensively investigate two-step shape invariance in the framework of $$\mathcal{N}$$-fold supersymmetry. We first show that any two-step shape-invariant system possesses type A 2-fold…

### Central Charge Extended Supersymmetric Structures for Fundamental Fermions Around Non-Abelian Vortices

- Physics
- 2014

Fermionic zero modes around non-abelian vortices are shown that they constitute two N = 2, d = 1 supersymmetric quantum mechanics algebras. These two algebras can be combined under certain…

### Extended Supersymmetries and 2 + 1 Dimensional Supersymmetric Chern Simons Theories

- Physics
- 2013

We study N = 2 supersymmetric Chern-Simons Higgs models in (2+1)-dimensions. As we will demonstrate, an extended supersymmetric quantum mechanics algebras underlies the fermionic zero modes quantum…

### Localized fermions on domain walls and extended supersymmetric quantum mechanics

- Physics
- 2013

We study fermionic fields localized on topologically unstable domain walls bounded by strings in a grand unified theory theoretical framework. Particularly, we found that the localized fermionic…

## References

SHOWING 1-10 OF 40 REFERENCES

### $\cN$-FOLD SUPERSYMMETRY IN QUANTUM MECHANICAL MATRIX MODELS

- Physics
- 2012

We formulate -fold supersymmetry in quantum mechanical matrix models. As an example, we construct general two-by-two Hermitian matrix two-fold supersymmetric quantum mechanical systems. We find that…

### {\cal N} -fold supersymmetry in quantum systems with position-dependent mass

- Physics
- 2006

We formulate the framework of -fold supersymmetry in one-body quantum mechanical systems with position-dependent mass (PDM). We show that some of the significant properties in the constant-mass case…

### 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…

### Nonlinear supersymmetry in quantum mechanics: Algebraic properties and differential representation

- Mathematics, Physics
- 2003

### A novel multi-parameter family of quantum systems with partially broken N-fold supersymmetry

- Mathematics
- 2005

We develop a systematic algorithm for constructing an -fold supersymmetric system from a given vector space invariant under one of the supercharges. Applying this algorithm to spaces of monomials, we…

### N-fold supersymmetry and quasi-solvability associated with X2-Laguerre polynomials

- Mathematics
- 2010

We construct a new family of quasi-solvable and N-fold supersymmetric quantum systems where each Hamiltonian preserves an exceptional polynomial subspace of codimension 2. We show that the family…

### Supersymmetric quantum mechanics with reflections

- Physics
- 2011

We consider a realization of supersymmetric quantum mechanics where supercharges are differential-difference operators with reflections. A supersymmetric system with an extended Scarf I potential is…

### Matrix superpotentials

- Mathematics, Physics
- 2011

We present a collection of matrix-valued shape invariant potentials which give rise to new exactly solvable problems of SUSY quantum mechanics. It includes all irreducible matrix superpotentials of…