An intertwining operator for the harmonic oscillator and the Dirac operator with application to the heat and wave kernels

TL;DR

This paper constructs an intertwining operator linking the harmonic oscillator to the Dirac operator, providing explicit solutions for heat and wave equations, and computing their kernels for both operators.

Contribution

It introduces a novel intertwining operator connecting the harmonic oscillator and Dirac operator, enabling explicit kernel computations for heat and wave equations.

Findings

Explicit heat and wave kernels for the Dirac operator

Computed heat and wave kernels for the harmonic oscillator

Established a new operator linking harmonic oscillator and Dirac operator

Abstract

In this article an intertwining operator is constructed which transforms the harmonic oscillator to the Dirac operator (the first order derivative operator). We give also the explicit solutions to the heat and wave equation associated to Dirac operator. As an application the heat and the wave kernels of the harmonic oscillator are computed.