General first-order mass ladder operators for Klein-Gordon fields

TL;DR

This paper derives the most general form of first-order ladder operators for Klein-Gordon fields, revealing new cases and connections to supersymmetric quantum mechanics, thus advancing the understanding of scalar field solutions.

Contribution

It provides the general conditions for first-order mass ladder operators for Klein-Gordon fields, including a previously unexplored non-trivial case.

Findings

Derived the general form of first-order ladder operators for Klein-Gordon fields.

Identified a new non-trivial case not discussed in prior work.

Explored the connection between ladder operators and supersymmetric quantum mechanics.

Abstract

We study the ladder operator on scalar fields, mapping a solution of the Klein-Gordon equation onto another solution with a different mass, when the operator is at most first order in derivatives. Imposing the commutation relation between the d'Alembertian, we obtain the general condition for the ladder operator, which contains a non-trivial case which was not discussed in the previous work [V. Cardoso, T. Houri and M. Kimura, Phys.Rev.D 96, 024044 (2017), arXiv:1706.07339]. We also discuss the relation with supersymmetric quantum mechanics.