Local Scale Invariance in Quantum Theory: A Non-Hermitian Pilot-Wave Formulation
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Quantum Physics arXiv:2601.03567 (quant-ph) [Submitted on 7 Jan 2026] Title:Local Scale Invariance in Quantum Theory: A Non-Hermitian Pilot-Wave Formulation Authors:Indrajit Sen, Matthew Leifer View a PDF of the paper titled Local Scale Invariance in Quantum Theory: A Non-Hermitian Pilot-Wave Formulation, by Indrajit Sen and Matthew Leifer View PDF Abstract:We show that Weyl's abandoned idea of local scale invariance has a natural realization at the quantum level in pilot-wave (deBroglie-Bohm) theory. We obtain the Weyl covariant derivative by complexifying the electromagnetic gauge coupling parameter. The resultant non-hermiticity has a natural interpretation in terms of local scale invariance of the quantum state in pilot-wave theory. The conserved current density is modified from $|\psi|^2$ to the local scale invariant, trajectory-dependent ratio $|\psi|^2/ \mathbf{1}^2[\mathcal{C}]$, where $\mathbf 1[\mathcal C]$ is a scale factor that depends on the pilot-wave trajectory $\mathcal C$ in configuration space. Our approach is general, and we implement it for the Schrödinger, Pauli, and Dirac equations coupled to an external electromagnetic field. We also implement it in quantum field theory for the case of a quantized axion field interacting with a quantized electromagnetic field. We discuss the equilibrium probability density and show that the corresponding trajectories are unique. Comments: Subjects: Quantum Physics (quant-ph); General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th); History and Philosophy of Physics (physics.hist-ph) Cite as: arXiv:2601.03567 [quant-ph] (or arXiv:2601.03567v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2601.03567 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Indrajit Sen [view email] [v1] Wed, 7 Jan 2026 04:27:59 UTC (2,168 KB) Full-text links: Access Paper: View a PDF of the paper titled Local Scale Invariance in Quantum Theory: A Non-Hermitian Pilot-Wave Formulation, by Indrajit Sen and Matthew LeiferView PDFTeX Source view license Current browse context: quant-ph new | recent | 2026-01 Change to browse by: gr-qc hep-th physics physics.hist-ph References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) Links to Code Toggle Papers with Code (What is Papers with Code?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)