Cauchy-Schwarz bound on the accuracy of truncated models in non-relativistic quantum electrodynamics

Daniel Eyles; Adam Stokes; Ahsan Nazir

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arXiv · 2503.07791

Cauchy-Schwarz bound on the accuracy of truncated models in non-relativistic quantum electrodynamics

Daniel Eyles·Adam Stokes·Ahsan Nazir

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Abstract

We show that the Cauchy-Schwarz inequality provides a simple yet general bound that limits the accuracy of light-matter theories which retain only finite numbers of material energy levels. A corollary is that unitary rotations within a truncated space cannot transform between gauges, because the contrary assumption yields incorrect predictions. In particular, a widespread model obtained using such a rotation and treated as a Coulomb gauge model within a substantial body of literature, yields incorrect predictions under this assumption. The simplest system of a single dipole coupled to a single photonic mode in one spatial dimension is analysed in detail.

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Daniel Eyles, Adam Stokes, Ahsan Nazir. 2025-03-10. Cauchy-Schwarz bound on the accuracy of truncated models in non-relativistic quantum electrodynamics. https://arxiv.org/abs/2503.07791

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