Can Quantum Field Theory be Recovered from Time-Symmetric Stochastic Mechanics? Part I: Generalizing the Liouville Equation
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Quantum Physics arXiv:2603.20399 (quant-ph) [Submitted on 20 Mar 2026] Title:Can Quantum Field Theory be Recovered from Time-Symmetric Stochastic Mechanics? Part I: Generalizing the Liouville Equation Authors:Simon Friederich, Mritunjay Tyagi View a PDF of the paper titled Can Quantum Field Theory be Recovered from Time-Symmetric Stochastic Mechanics? Part I: Generalizing the Liouville Equation, by Simon Friederich and 1 other authors View PDF HTML (experimental) Abstract:We explore whether quantum field theory can be understood as the statistical mechanics of a time-reversal-invariant stochastic generalization of Hamiltonian dynamics. The motivation for this project, started with this paper, is to assign sharp values to all observables and thereby avoid the quantum measurement problem. In classical mechanics, motion is deterministic and corresponds to an evolution of the phase space probability density according to Liouville's equation that is governed by first derivatives of the Hamiltonian in phase space. We derive a generalization of the Liouville equation with natural constraints -- namely, reduction to classical Hamiltonian dynamics as the stochasticity parameter $\hbar\mapsto0$, Fokker-Planck form for the probability density evolution, local Hamiltonian dependence, time-reversal invariance, energy conservation, and minimality -- which turns out to be a Fokker-Planck equation with a generalized diffusion matrix that is symmetric, traceless, and constructed from the Hessian of the Hamiltonian. We then show that the Schrödinger equation in the coherent-state phase-space formulation of certain bosonic QFTs has precisely this form, with the Husimi function playing the role of the phase space probability density. The question to what extent this equation can be interpreted in terms of objective stochastic field theories is discussed in a companion paper. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2603.20399 [quant-ph] (or arXiv:2603.20399v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2603.20399 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Simon Friederich [view email] [v1] Fri, 20 Mar 2026 18:19:21 UTC (38 KB) Full-text links: Access Paper: View a PDF of the paper titled Can Quantum Field Theory be Recovered from Time-Symmetric Stochastic Mechanics? Part I: Generalizing the Liouville Equation, by Simon Friederich and 1 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-03 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?)