Higher-Order Derivative Susy in Quantum Mechanics with Large Energy Shifts

TL;DR

This paper explores higher-order derivative supersymmetry in quantum mechanics, focusing on large energy shifts between states and their implications for SUSY breaking and potential toy models.

Contribution

It introduces a method using the 'gluing' procedure to realize large energy shifts in second order derivative SUSYQM and examines the infinite energy shift limit.

Findings

Large energy shifts can be incorporated without breaking SUSY at low energies.

Comparison between higher derivative SUSY algebra and standard SUSY algebra.

Potential for constructing toy models with significant fermion-boson energy splittings.

Abstract

Within the framework of second order derivative (one dimensional) SUSYQM we discuss particular realizations which incorporate large energy shifts between the lowest states of the spectrum of the superhamiltonian (of Schr\"odinger type). The technique used in this construction is based on the "gluing" procedure. We study the limit of infinite energy shift for the charges of the Higher Derivative SUSY Algebra, and compare the results with those of the standard SUSY Algebra. We conjecture that our results can suggest a construction of a toy model where large energy splittings between fermionic and bosonic partners do not affect the SUSY at low energies.