Ladder Operators in Repulsive Harmonic Oscillator with Application to the Schwinger Effect

TL;DR

This paper introduces an algebraic method to define ladder operators for the repulsive harmonic oscillator, enabling a new approach to analyze phenomena like the Schwinger effect and supersymmetric extensions.

Contribution

It presents a novel algebraic formalism for repulsive harmonic oscillators, connecting it to the Schwinger effect and supersymmetry, and reproduces known solutions.

Findings

Algebraic ladder operators for repulsive harmonic oscillators are constructed.

The formalism successfully reproduces known analytic solutions.

Application to charged particles in electric fields related to the Schwinger effect.

Abstract

The ladder operators in harmonic oscillator are a well-known strong tool for various problems in physics. In the same sense, it is sometimes expected to handle the problems of repulsive harmonic oscillator in a similar way to the ladder operators in harmonic oscillators, though their analytic solutions are well known. In this paper, we discuss a simple algebraic way to introduce the ladder operators of the repulsive harmonic oscillators, which can reproduce well-known analytic solutions. Applying this formalism, we discuss the charged particles in a constant electric field in relation to the Schwinger effect; the discussion is also made on a supersymmetric extension of this formalism.