Abstract
Supersymmetry plays a main role in all current thinking about superstring theory. Indeed, many remarkable properties of string theory have been explained using supersymmetry as a tool. So far, there has beenno unbroken supersymmetry observed in nature, and if nature is described by supersymmetry, it must bebroken. Supersymmetry may be broken spontaneously at any order of perturbation theory or dynamicallydue to nonperturbative effects. To examine the methods of supersymmetry breaking, special attention isgiven to discuss the normalization of the ground state of the supersymmetric harmonic oscillator. Thisstudy explains that perturbation theory gives incorrect results for both the ground-state wave functionand the energy spectrum and it fails to give an explanation to the supersymmetry breaking.
Highlights
Supersymmetry, often abbreviated SUSY, was first introduced in 1971 by Gelfand and Likhtman, Raymond, and Neveu and Schwartz, and later, it was rediscovered by other groups [1, 2]
To examine the methods of supersymmetry breaking, we study the normalization of the ground state of the supersymmetric harmonic oscillator and calculate the corrections to the ground-state energy using perturbation theory
We studied the basic aspects of supersymmetric quantum mechanics
Summary
Supersymmetry, often abbreviated SUSY, was first introduced in 1971 by Gelfand and Likhtman, Raymond, and Neveu and Schwartz, and later, it was rediscovered by other groups [1, 2]. The main mathematical structure which involves supersymmetric quantum mechanics is derived starting with explaining the basic idea of supersymmetry and followed by introducing the necessary framework to make a supersymmetric theory. We show that if there is a supersymmetric state, it is the zero-energy ground-state If such a state exists, the supersymmetry is unbroken; otherwise, it is broken. To examine the methods of supersymmetry breaking, we study the normalization of the ground state of the supersymmetric harmonic oscillator and calculate the corrections to the ground-state energy using perturbation theory. We give a general background in the concepts and methods of supersymmetric quantum mechanics This followed by providing a more specific study of the ground state of the supersymmetric harmonic oscillator.
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