Is there a problem with our Hamiltonians for quantum nonlinear optical processes?

TL;DR

This paper identifies a mathematical flaw in common Hamiltonian models for quantum nonlinear optical processes, proposes a fix, and explains why these models remain useful despite the flaw.

Contribution

It reveals a flaw in standard Hamiltonians for quantum nonlinear optics, offers a correction, and justifies their continued use.

Findings

Identified a mathematical flaw in existing models

Proposed a method to fix the flaw

Justified continued use of current Hamiltonians

Abstract

The models we use, habitually, to describe quantum nonlinear optical processes have been remarkably successful yet, with few exceptions, they each contain a mathematical flaw. We present this flaw, show how it can be fixed and, in the process, suggest why we can continue to use our favoured Hamiltonians.