Canonical Formulation and Conservation Laws of an AbelianInformation–Gauge EFTCoupled to a Scalar Potential

Canonical Formulation and Conservation Laws of an AbelianInformation–Gauge EFTCoupled to a Scalar Potential | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Canonical Formulation and Conservation Laws of an AbelianInformation–Gauge EFTCoupled to a Scalar Potential Ju Hyung Lee This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8728299/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract We formulate a conservative effective field theory (EFT) in which an Abelian information–gaugesector U(1)Λ, carried by a connection Λµ, couples to a coarse-grained local entropy/nonequilibriumpotential σ(x) and to a conserved gauge-source current Jµinfo. Here σ(x) is a platform-defined coarsegrained state variable; mappings like σ = ln(T/T0) or ln(n/n0) are optional operational proxies forspecific protocols only. Nonlocal entanglement entropy is used only as semiclassical motivation;locality, power counting, and symmetry control are implemented through gauge-invariant operatorsbuilt from the curvature Fµν = ∇µΛν −∇νΛµ and the covariant gradients ∇µσ.From a covariant action principle we obtain the IR/EFT metric field equation Gµν + Λccgµν =8πGc4T(m)µν +T(Λ)µν +T(σ)µν , where T(Λ)µν is the manifestly gauge-invariant Maxwell stress tensor andthe interaction gΛJµinfoΛµ is kept in the matter/entropy sector. Variation with respect to Λµyields the Maxwell-like equation ∇µFµν = gΛJνinfo, and its divergence implies the Noether identity∇µJµinfo = 0 in the minimal anomaly-free EFT. A controlled nonrelativistic reduction reproducesSchrödinger dynamics in which Λµ acts as a phase connection; accordingly, Wilson phases and thecurvature Fµν are the primary gauge-invariant observables.Near dynamical criticality we parameterize state-/environment-dependent scaling by γth(ξ) =(ξ/ξ0)∆η, interpreted as an in-medium scaling factor within a specified near-critical/open-systemregime rather than a universal modification of vacuum Lorentz invariance. In the nonrelativisticsector, minimal coupling to the U(1)Λ connection induces a magnetic-type symplectic structure,equivalently controlling the noncommutativity of kinetic momenta through [ˆ Πi, ˆ Πj] = iℏgΛFij. Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8728299","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":583039648,"identity":"13a3b9f1-24fc-4930-a7f4-131afc93cdeb","order_by":0,"name":"Ju Hyung Lee","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA0ElEQVRIiWNgGAWjYDACCQYGZjCDvQFIGFgQ1sEjwcDYDGEdAGmRIEWLRALUUkLAXrr5+OOCP3ZyujOfX93wo0CCgb+9OwG/LTLHEptntiUbm93OKbvZA3SYxJmzGwg4LMewmbeBOXHb7Zy0GzxALQYSuURo4flTX7/t5pm0m3+I18J2OMHsBvux28TZciMtcTZv23HDbWdy2G7LGEjwEPQL+4zkA595/lTLmx0//uzmmz82cvztvfi1IFtoACaJVQ628AEpqkfBKBgFo2AEAQBOBkY2IhTBHQAAAABJRU5ErkJggg==","orcid":"","institution":"XFC inc.","correspondingAuthor":true,"prefix":"","firstName":"Ju","middleName":"Hyung","lastName":"Lee","suffix":""}],"badges":[],"createdAt":"2026-01-29 07:23:48","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8728299/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8728299/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":101753402,"identity":"7f748e7f-e551-495f-b167-97401348217c","added_by":"auto","created_at":"2026-02-03 10:39:59","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":877215,"visible":true,"origin":"","legend":"","description":"","filename":"IGEFTIJTP.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8728299/v1_covered_b6690425-30bf-4730-98fd-5bea8571f7a4.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Canonical Formulation and Conservation Laws of an AbelianInformation–Gauge EFTCoupled to a Scalar Potential","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-8728299/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8728299/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"We formulate a conservative effective field theory (EFT) in which an Abelian information–gaugesector U(1)Λ, carried by a connection Λµ, couples to a coarse-grained local entropy/nonequilibriumpotential σ(x) and to a conserved gauge-source current Jµinfo. Here σ(x) is a platform-defined coarsegrained state variable; mappings like σ = ln(T/T0) or ln(n/n0) are optional operational proxies forspecific protocols only. Nonlocal entanglement entropy is used only as semiclassical motivation;locality, power counting, and symmetry control are implemented through gauge-invariant operatorsbuilt from the curvature Fµν = ∇µΛν −∇νΛµ and the covariant gradients ∇µσ.From a covariant action principle we obtain the IR/EFT metric field equation Gµν + Λccgµν =8πGc4T(m)µν +T(Λ)µν +T(σ)µν , where T(Λ)µν is the manifestly gauge-invariant Maxwell stress tensor andthe interaction gΛJµinfoΛµ is kept in the matter/entropy sector. Variation with respect to Λµyields the Maxwell-like equation ∇µFµν = gΛJνinfo, and its divergence implies the Noether identity∇µJµinfo = 0 in the minimal anomaly-free EFT. A controlled nonrelativistic reduction reproducesSchrödinger dynamics in which Λµ acts as a phase connection; accordingly, Wilson phases and thecurvature Fµν are the primary gauge-invariant observables.Near dynamical criticality we parameterize state-/environment-dependent scaling by γth(ξ) =(ξ/ξ0)∆η, interpreted as an in-medium scaling factor within a specified near-critical/open-systemregime rather than a universal modification of vacuum Lorentz invariance. In the nonrelativisticsector, minimal coupling to the U(1)Λ connection induces a magnetic-type symplectic structure,equivalently controlling the noncommutativity of kinetic momenta through [ˆ Πi, ˆ Πj] = iℏgΛFij.","manuscriptTitle":"Canonical Formulation and Conservation Laws of an AbelianInformation–Gauge EFTCoupled to a Scalar Potential","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-02-02 04:48:13","doi":"10.21203/rs.3.rs-8728299/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"7c8dfdf6-2bc0-495b-bbcb-7bf00bec5c40","owner":[],"postedDate":"February 2nd, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2026-02-02T04:48:13+00:00","versionOfRecord":[],"versionCreatedAt":"2026-02-02 04:48:13","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8728299","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8728299","identity":"rs-8728299","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}