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

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 (Cardoso et al 2017 Phys. Rev. D 96 024044). We also discuss the relation with supersymmetric quantum mechanics.