{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T19:02:49Z","timestamp":1790881369805,"version":"4.1.0"},"reference-count":63,"publisher":"American Physical Society (APS)","issue":"2","license":[{"start":{"date-parts":[[2026,8,14]],"date-time":"2026-08-14T00:00:00Z","timestamp":1786665600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["551294732"],"award-info":[{"award-number":["551294732"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["journals.aps.org"],"crossmark-restriction":true},"short-container-title":["Phys. Rev. E"],"accepted":{"date-parts":[[2026,7,24]]},"abstract":"<jats:p>We address gauge invariance in the statistical mechanics of quantum many-body systems. The gauge transformation acts on the position and momentum degrees of freedom, and it is represented by a quantum shifting superoperator that maps quantum observables onto each other. The shifting superoperator is anti-self-adjoint, and it has noncommutative Lie algebra structure. These properties induce exact equilibrium sum rules that connect locally resolved force and hyperforce densities for any given observable. We argue that the framework is amenable to tight integration into quantum hyperdensity functional theory and that it generalizes naturally to nonequilibrium.<\/jats:p>","DOI":"10.1103\/dzz3-m28k","type":"journal-article","created":{"date-parts":[[2026,7,24]],"date-time":"2026-07-24T14:00:31Z","timestamp":1784901631000},"update-policy":"https:\/\/doi.org\/10.1103\/crossmark-policy","source":"Crossref","is-referenced-by-count":3,"title":["Quantum statistical mechanical gauge invariance"],"prefix":"10.1103","volume":"114","author":[{"ORCID":"https:\/\/orcid.org\/0009-0007-2490-7562","authenticated-orcid":true,"given":"Johanna","family":"M\u00fcller","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/0234wmv40","id-type":"ROR","asserted-by":"publisher"}],"name":"Universit\u00e4t Bayreuth"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5015-2972","authenticated-orcid":true,"given":"Matthias","family":"Schmidt","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/0234wmv40","id-type":"ROR","asserted-by":"publisher"}],"name":"Universit\u00e4t Bayreuth"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"16","published-online":{"date-parts":[[2026,8,14]]},"reference":[{"key":"dzz3-m28kCc1R1","doi-asserted-by":"publisher","DOI":"10.1103\/RevModPhys.72.1","type":"journal-article"},{"key":"dzz3-m28kCc2R1","doi-asserted-by":"publisher","DOI":"10.1103\/RevModPhys.73.663","type":"journal-article"},{"key":"dzz3-m28kCc3R1","unstructured":"E. Noether, Invariante Variationsprobleme, Nachr. K\u00f6nig. Gesellsch. Wiss. G\u00f6ttingen, Math.-Phys. Klasse 235, 83 (1918)","type":"journal-article"},{"key":"dzz3-m28kCc3R2","doi-asserted-by":"publisher","DOI":"10.1080\/00411457108231446","type":"journal-article"},{"key":"dzz3-m28kCc4R1","doi-asserted-by":"publisher","DOI":"10.1063\/1.4773921","type":"journal-article"},{"key":"dzz3-m28kCc5R1","doi-asserted-by":"publisher","DOI":"10.1038\/ncomms4821","type":"journal-article"},{"key":"dzz3-m28kCc6R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.116.140601","type":"journal-article"},{"key":"dzz3-m28kCc7R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.99.022109","type":"journal-article"},{"key":"dzz3-m28kCc8R1","doi-asserted-by":"publisher","DOI":"10.3390\/e25071082","type":"journal-article"},{"key":"dzz3-m28kCc9R1","doi-asserted-by":"publisher","DOI":"10.1088\/1742-5468\/ac6a5b","type":"journal-article"},{"key":"dzz3-m28kCc10R1","doi-asserted-by":"publisher","DOI":"10.1063\/5.0148466","type":"journal-article"},{"key":"dzz3-m28kCc11R1","doi-asserted-by":"publisher","DOI":"10.2140\/memocs.2025.13.1","type":"journal-article"},{"key":"dzz3-m28kCc12R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.133.217101","type":"journal-article"},{"key":"dzz3-m28kCc12R2","unstructured":"Editors&#39; Suggestion; Phys. Rev. Lett.&#39;s Collection of the Year 2024;","type":"other"},{"key":"dzz3-m28kCc12R3","first-page":"163","type":"journal-article","volume":"17","year":"2024","journal-title":"Featured in Physics"},{"key":"dzz3-m28kCc13R1","doi-asserted-by":"publisher","DOI":"10.1088\/1751-8121\/adbfe6","type":"journal-article"},{"key":"dzz3-m28kCc14R1","doi-asserted-by":"publisher","DOI":"10.1103\/Physics.17.163","type":"journal-article"},{"key":"dzz3-m28kCc15R1","doi-asserted-by":"publisher","DOI":"10.1063\/pt.wcgt.sirc","type":"journal-article"},{"key":"dzz3-m28kCc17R1","doi-asserted-by":"publisher","DOI":"10.1038\/s42005-021-00669-2","type":"journal-article"},{"key":"dzz3-m28kCc18R1","doi-asserted-by":"publisher","DOI":"10.1038\/s42005-024-01568-y","type":"journal-article"},{"key":"dzz3-m28kCc19R1","doi-asserted-by":"publisher","DOI":"10.1088\/1751-8121\/aca12d","type":"journal-article"},{"key":"dzz3-m28kCc20R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.130.268203","type":"journal-article"},{"key":"dzz3-m28kCc21R1","volume-title":"La Th\u00e9orie Statistique Des Fluides et L'\u00e9quation D'\u00e9tat","author":"J. Yvon","year":"1935","type":"book"},{"key":"dzz3-m28kCc22R1","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.1946.0093","type":"journal-article"},{"key":"dzz3-m28kCc23R1","volume-title":"Theory of Simple Liquids","author":"J.\u00a0P. Hansen","year":"2013","type":"book"},{"key":"dzz3-m28kCc24R1","doi-asserted-by":"publisher","DOI":"10.1103\/8rks-wg7f","type":"journal-article"},{"key":"dzz3-m28kCc25R1","doi-asserted-by":"publisher","DOI":"10.1103\/RevModPhys.80.885","type":"journal-article"},{"key":"dzz3-m28kCc26R1","doi-asserted-by":"publisher","DOI":"10.1126\/science.aaf8834","type":"journal-article"},{"key":"dzz3-m28kCc27R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevX.7.041047","type":"journal-article"},{"key":"dzz3-m28kCc28R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.119.073002","type":"journal-article"},{"key":"dzz3-m28kCc29R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.95.053624","type":"journal-article"},{"key":"dzz3-m28kCc30R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.131.060401","type":"journal-article"},{"key":"dzz3-m28kCc33R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.110.062203","type":"journal-article"},{"key":"dzz3-m28kCc34R1","doi-asserted-by":"publisher","DOI":"10.1088\/2058-9565\/ae6a1b","type":"journal-article"},{"key":"dzz3-m28kCc35R1","doi-asserted-by":"publisher","DOI":"10.1063\/5.0297117","type":"journal-article"},{"key":"dzz3-m28kCc36R1","doi-asserted-by":"publisher","DOI":"10.1103\/RevModPhys.94.015007","type":"journal-article"},{"key":"dzz3-m28kCc37R1","volume-title":"The Principles of Quantum Mechanics","author":"P.\u00a0A.\u00a0M. Dirac","year":"1958","type":"book"},{"key":"dzz3-m28kCc38R1","volume-title":"Advanced Quantum Mechanics","author":"J.\u00a0J. Sakurai","year":"1973","type":"book"},{"key":"dzz3-m28kCc39R1","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-83715-9","type":"book","volume-title":"The Quantum Statistics of Dynamic Processes","author":"E. Fick","year":"1990"},{"key":"dzz3-m28kCc40R1","doi-asserted-by":"publisher","DOI":"10.1006\/aphy.1994.1055","type":"journal-article"},{"key":"dzz3-m28kCc41R1","volume-title":"Classical Mechanics","author":"H. Goldstein","year":"2002","type":"book"},{"key":"dzz3-m28kCc42R1","doi-asserted-by":"publisher","DOI":"10.1143\/JPSJ.12.570","type":"journal-article"},{"key":"dzz3-m28kCc43R1","doi-asserted-by":"publisher","DOI":"10.1007\/BF00739578","type":"journal-article"},{"key":"dzz3-m28kCc44R1","doi-asserted-by":"publisher","DOI":"10.1016\/0378-4371(95)00385-1","type":"journal-article"},{"key":"dzz3-m28kCc45R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.133.098201","type":"journal-article"},{"key":"dzz3-m28kCc46R1","doi-asserted-by":"publisher","DOI":"10.1088\/1361-648X\/ad98da","type":"journal-article"},{"key":"dzz3-m28kCc47R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRev.137.A1441","type":"journal-article"},{"key":"dzz3-m28kCc48R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.71.165104","type":"journal-article"},{"key":"dzz3-m28kCc49R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.71.165105","type":"journal-article"},{"key":"dzz3-m28kCc50R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.75.125105","type":"journal-article"},{"key":"dzz3-m28kCc51R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.73.235102","type":"journal-article"},{"key":"dzz3-m28kCc52R1","doi-asserted-by":"publisher","DOI":"10.1063\/5.0039962","type":"journal-article"},{"key":"dzz3-m28kCc53R1","doi-asserted-by":"publisher","DOI":"10.1063\/1.5123608","type":"journal-article"},{"key":"dzz3-m28kCc54R1","doi-asserted-by":"publisher","DOI":"10.1103\/q7dh-ccch","type":"journal-article"},{"key":"dzz3-m28kCc55R1","doi-asserted-by":"publisher","DOI":"10.1063\/1.1740082","type":"journal-article"},{"key":"dzz3-m28kCc56R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.69.026115","type":"journal-article"},{"key":"dzz3-m28kCc57R1","doi-asserted-by":"publisher","DOI":"10.3390\/e26020111","type":"journal-article"},{"key":"dzz3-m28kCc58R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.111.052209","type":"journal-article"},{"key":"dzz3-m28kCc59R1","doi-asserted-by":"publisher","DOI":"10.1103\/4k95-qv87","type":"journal-article"},{"key":"dzz3-m28kCc60R1","doi-asserted-by":"publisher","DOI":"10.1103\/hvkc-djyj","type":"journal-article"},{"key":"dzz3-m28kCc62R1","doi-asserted-by":"publisher","DOI":"10.1103\/jb7b-rsfb","type":"journal-article"},{"key":"dzz3-m28kCc63R1","doi-asserted-by":"publisher","DOI":"10.1103\/vghs-2pdw","type":"journal-article"},{"key":"dzz3-m28kCc64R1","unstructured":"https:\/\/www.mschmidt.uni-bayreuth.de\/pubs\/quantum_gauge.nb.","type":"other"}],"container-title":["Physical Review E"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.aps.org\/article\/10.1103\/dzz3-m28k","content-type":"unspecified","content-version":"vor","intended-application":"syndication"},{"URL":"http:\/\/harvest.aps.org\/v2\/journals\/articles\/10.1103\/dzz3-m28k\/fulltext","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T18:16:29Z","timestamp":1790878589000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.aps.org\/doi\/10.1103\/dzz3-m28k"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,8,14]]},"references-count":63,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2026,8]]}},"URL":"https:\/\/doi.org\/10.1103\/dzz3-m28k","relation":{"has-preprint":[{"id-type":"doi","id":"10.48550\/arXiv.2509.20494","asserted-by":"subject"}]},"ISSN":["2470-0045","2470-0053"],"issn-type":[{"value":"2470-0045","type":"print"},{"value":"2470-0053","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,8,14]]},"assertion":[{"value":"2025-09-24","name":"date_received","label":"Date Received","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"Published by the American Physical Society. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright_statement","label":"Copyright statement","group":{"name":"copyright","label":"copyright"}},{"value":"2026","name":"copyright_year","label":"Copyright year","group":{"name":"copyright","label":"copyright"}},{"value":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/","name":"creative_commons_license","label":"Creative Commons license","group":{"name":"licenses","label":"Licenses"}},{"value":"\u00a92026 The authors","name":"copyright_holder","label":"Copyright holder","group":{"name":"copyright","label":"copyright"}}],"article-number":"L022104"}}