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

• URL: http://arxiv.org/abs/2503.07791v1
• Date: Mon, 10 Mar 2025 19:14:41 GMT
• Title: Cauchy-Schwarz bound on the accuracy of truncated models in non-relativistic quantum electrodynamics
• Authors: Daniel Eyles, Adam Stokes, Ahsan Nazir,
• Abstract summary: We show that the Cauchy-Schwarz inequality limits the accuracy of light-matter theories which retain only finite numbers of material energy levels.<n>A corollary is that unitary rotations within a truncated space cannot transform between gauges, because the contrary assumption yields incorrect predictions.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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