The Dirac factorization method and the harmonic oscillator

TL;DR

This paper explores the application of the Dirac factorization method to harmonic oscillators, revealing a natural supersymmetric formulation and proposing a novel physical interpretation involving vacuum fluctuations and spontaneous emission.

Contribution

It introduces a supersymmetric approach to harmonic oscillators via Dirac factorization and suggests a new physical perspective on vacuum fluctuations.

Findings

Dirac factorization leads to supersymmetric formulations.

Vacuum fluctuations may be viewed as spontaneous emission.

Quantization arises from noncommuting variables.

Abstract

We apply the Dirac factorization method to the nonrelativistic harmonic oscillator and, more in general, to Hamiltonians with a generic potential. It is shown that this procedure naturally leads to a supersymmetric formulation of the problems under study. It is also speculated on the physical meaning underlying this method and it is suggested that the vacuum field fluctuations can be viewed as the spontaneous emission of the associated two-level system, whose quantization is due to the noncommuting nature of the harmonic oscillator canonical variables.