Tagged vector space, Part II: function space index and the implied functional integration measure

Quantum Physics arXiv:2511.05974 (quant-ph) [Submitted on 8 Nov 2025] Title:Tagged vector space, Part II: function space index and the implied functional integration measure Authors:Filippus S. Roux View a PDF of the paper titled Tagged vector space, Part II: function space index and the implied functional integration measure, by Filippus S. Roux View PDF HTML (experimental) Abstract:The definition of quantum states in terms of tagged vector spaces is generalized to incorporate the spatiotemporal and spin degrees of freedom. Considering a tagged vector space where the index space is a function space, representing the additional degrees of freedom, we obtained axioms for the tags that include a completeness condition expressed in terms of a functional integral with an abstract functional integration measure. Using these axioms, we derive a generating functional for the moments of this functional integration measure. These moments are then used to evaluate the functional integrals of Gaussian functionals, leading to expressions in accordance with those obtained as generalizations of equivalent integrals over a finite number of integration variables. For a Gaussian functional used as a probability distributions, we show that its moments, obtained with this functional integration measure, satisfy Carleman's condition, indicating that the measure is unique. Comments: Subjects: Quantum Physics (quant-ph); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph) Cite as: arXiv:2511.05974 [quant-ph] (or arXiv:2511.05974v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2511.05974 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: F. Stef Roux [view email] [v1] Sat, 8 Nov 2025 11:40:28 UTC (29 KB) Full-text links: Access Paper: View a PDF of the paper titled Tagged vector space, Part II: function space index and the implied functional integration measure, by Filippus S. RouxView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2025-11 Change to browse by: hep-th math math-ph math.MP 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?)