{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,10]],"date-time":"2026-09-10T00:16:31Z","timestamp":1788999391847,"version":"build-2803163510"},"reference-count":138,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2023,12,24]],"date-time":"2023-12-24T00:00:00Z","timestamp":1703376000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Explicit and spontaneous breaking of spacetime symmetry under diffeomorphisms, local translations, and local Lorentz transformations due to the presence of fixed background fields is examined in Einstein\u2013Cartan theory. In particular, the roles of torsion and violation of local translation invariance are highlighted. The nature of the types of background fields that can arise and how they cause spacetime symmetry breaking is discussed. With explicit breaking, potential no-go results are known to exist, which if not evaded lead to inconsistencies between the Bianchi identities, Noether identities, and the equations of motion. These are examined in detail, and the effects of nondynamical backgrounds and explicit breaking on the energy\u2013momentum tensor when torsion is present are discussed as well. Examples illustrating various features of both explicit and spontaneous breaking of local translations are presented and compared to the case of diffeomorphism breaking.<\/jats:p>","DOI":"10.3390\/sym16010025","type":"journal-article","created":{"date-parts":[[2023,12,24]],"date-time":"2023-12-24T20:44:15Z","timestamp":1703450655000},"page":"25","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Spontaneous and Explicit Spacetime Symmetry Breaking in Einstein\u2013Cartan Theory with Background Fields"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8415-9611","authenticated-orcid":false,"given":"Robert","family":"Bluhm","sequence":"first","affiliation":[{"name":"Department of Physics and Astronomy, Colby College, Waterville, ME 04901, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yu","family":"Zhi","sequence":"additional","affiliation":[{"name":"Department of Physics and Astronomy, Colby College, Waterville, ME 04901, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,12,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"325","DOI":"10.24033\/asens.751","article-title":"Sur les vari\u00e9t\u00e9s \u00e0 connexion affine et la th\u00e9orie de la relativit\u00e9 g\u00e9n\u00e9ralis\u00e9 (premi\u00e9re partie)","volume":"40","author":"Cartan","year":"1923","journal-title":"Ann. 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