{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,27]],"date-time":"2026-02-27T00:03:18Z","timestamp":1772150598802,"version":"3.50.1"},"reference-count":103,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2024,1,11]],"date-time":"2024-01-11T00:00:00Z","timestamp":1704931200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Higher Education and Science Committee of the Ministry of Education, Science, Culture and Sport RA","award":["21AG-1C047"],"award-info":[{"award-number":["21AG-1C047"]}]},{"name":"Higher Education and Science Committee of the Ministry of Education, Science, Culture and Sport RA","award":["23AN:PS-hepth-2889"],"award-info":[{"award-number":["23AN:PS-hepth-2889"]}]},{"name":"ANSEF","award":["21AG-1C047"],"award-info":[{"award-number":["21AG-1C047"]}]},{"name":"ANSEF","award":["23AN:PS-hepth-2889"],"award-info":[{"award-number":["23AN:PS-hepth-2889"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This paper presents a review of investigations into the vacuum expectation value of the current density for a charged scalar field in spacetimes that hold toroidally compactified spatial dimensions. As background geometries, the locally Minkowskian (LM), locally de Sitter (LdS), and locally anti-de Sitter (LAdS) spacetimes are considered. Along compact dimensions, quasi-periodicity conditions are imposed on the field operator and the presence of a constant gauge field is assumed. The vacuum current has nonzero components along the compact dimensions only. Those components are periodic functions of the magnetic flux enclosed in compact dimensions, with a period that is equal to the flux quantum. For LdS and LAdS geometries, and for small values of the length of a compact dimension, compared with the curvature radius, the leading term in the expansion of the the vacuum current along that dimension coincides with that for LM bulk. In this limit, the dominant contribution to the mode sum for the current density comes from the vacuum fluctuations with wavelengths smaller to those of the curvature radius; additionally, the influence of the gravitational field is weak. The effects of the gravitational field are essential for lengths of compact dimensions that are larger than the curvature radius. In particular, instead of the exponential suppression of the current density in LM bulk, one can obtain a power law decay in the LdS and LAdS spacetimes.<\/jats:p>","DOI":"10.3390\/sym16010092","type":"journal-article","created":{"date-parts":[[2024,1,11]],"date-time":"2024-01-11T08:27:07Z","timestamp":1704961627000},"page":"92","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Vacuum Currents for a Scalar Field in Models with Compact Dimensions"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6576-9895","authenticated-orcid":false,"given":"Aram A.","family":"Saharian","sequence":"first","affiliation":[{"name":"Institute of Physics, Yerevan State University, 1 Alex Manogian Street, Yerevan 0025, Armenia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,1,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1016\/0375-9601(79)90032-X","article-title":"Mass generation by self-interaction in non-Minkowskian spacetimes","volume":"70","author":"Ford","year":"1979","journal-title":"Phys. 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