{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:41:58Z","timestamp":1760240518771,"version":"build-2065373602"},"reference-count":25,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2019,7,4]],"date-time":"2019-07-04T00:00:00Z","timestamp":1562198400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003141","name":"Consejo Nacional de Ciencia y Tecnolog\u00eda","doi-asserted-by":"publisher","award":["38142"],"award-info":[{"award-number":["38142"]}],"id":[{"id":"10.13039\/501100003141","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>We define a family of observables for abelian Yang-Mills fields associated to compact regions     U \u2286 M     with smooth boundary in Riemannian manifolds. Each observable is parametrized by a first variation of solutions and arises as the integration of gauge invariant conserved current along admissible hypersurfaces contained in the region. The Poisson bracket uses the integration of a canonical multisymplectic current.<\/jats:p>","DOI":"10.3390\/sym11070880","type":"journal-article","created":{"date-parts":[[2019,7,4]],"date-time":"2019-07-04T11:13:18Z","timestamp":1562238798000},"page":"880","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A Poisson Algebra for Abelian Yang-Mills Fields on Riemannian Manifolds with Boundary"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2453-9049","authenticated-orcid":false,"given":"Homero G.","family":"D\u00edaz-Mar\u00edn","sequence":"first","affiliation":[{"name":"Facultad de Ciencias F\u00edsico-Matem\u00e1ticas, Universidad Michoacana de San Nicol\u00e1s de Hidalgo, Morelia C.P. 58060, Mexico"}]}],"member":"1968","published-online":{"date-parts":[[2019,7,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"203","DOI":"10.5802\/aif.451","article-title":"The Hamilton-Cartan formalism in the calculus of variations","volume":"23","author":"Goldschmidt","year":"1973","journal-title":"Annales de l\u2019Institut Fourier"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1007\/BF01645975","article-title":"A finite-dimensional canonical formalism in the classical field theory","volume":"30","author":"Kijowski","year":"1973","journal-title":"Commun. 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