{"@context":{"@vocab":"https://cir.nii.ac.jp/schema/1.0/","rdfs":"http://www.w3.org/2000/01/rdf-schema#","dc":"http://purl.org/dc/elements/1.1/","dcterms":"http://purl.org/dc/terms/","foaf":"http://xmlns.com/foaf/0.1/","prism":"http://prismstandard.org/namespaces/basic/2.0/","cinii":"http://ci.nii.ac.jp/ns/1.0/","datacite":"https://schema.datacite.org/meta/kernel-4/","ndl":"http://ndl.go.jp/dcndl/terms/","jpcoar":"https://github.com/JPCOAR/schema/blob/master/2.0/"},"@id":"https://cir.nii.ac.jp/crid/1361699996354829440.json","@type":"Article","productIdentifier":[{"identifier":{"@type":"DOI","@value":"10.3390/sym2020609"}},{"identifier":{"@type":"URI","@value":"https://www.mdpi.com/2073-8994/2/2/609/pdf"}}],"dc:title":[{"@value":"Spontaneous Symmetry Breaking and Nambu–Goldstone Bosons in Quantum Many-Body Systems"}],"description":[{"type":"abstract","notation":[{"@value":"<jats:p>Spontaneous symmetry breaking is a general principle that constitutes the underlying concept of a vast number of physical phenomena ranging from ferromagnetism and superconductivity in condensed matter physics to the Higgs mechanism in the standard model of elementary particles. I focus on manifestations of spontaneously broken symmetries in systems that are not Lorentz invariant, which include both nonrelativistic systems as well as relativistic systems at nonzero density, providing a self-contained review of the properties of spontaneously broken symmetries specific to such theories. Topics covered include: (i) Introduction to the mathematics of spontaneous symmetry breaking and the Goldstone theorem. (ii) Minimization of Higgs-type potentials for higher-dimensional representations. (iii) Counting rules for Nambu–Goldstone bosons and their dispersion relations. (iv) Construction of effective Lagrangians. Specific examples in both relativistic and nonrelativistic physics are worked out in detail.</jats:p>"}]}],"creator":[{"@id":"https://cir.nii.ac.jp/crid/1381699996354829440","@type":"Researcher","foaf:name":[{"@value":"Tomáš Brauner"}],"jpcoar:affiliationName":[{"@value":"Institute for Theoretical Physics, Goethe University, 60438 Frankfurt am Main, Germany"},{"@value":"Department of Theoretical Physics, Nuclear Physics Institute ASCR, 25068 Řež, Czech Republic"}]}],"publication":{"publicationIdentifier":[{"@type":"EISSN","@value":"20738994"},{"@type":"PISSN","@value":"https://id.crossref.org/issn/20738994"}],"prism:publicationName":[{"@value":"Symmetry"}],"dc:publisher":[{"@value":"MDPI AG"}],"prism:publicationDate":"2010-04-07","prism:volume":"2","prism:number":"2","prism:startingPage":"609","prism:endingPage":"657"},"reviewed":"false","dc:rights":["https://creativecommons.org/licenses/by/3.0/"],"url":[{"@id":"https://www.mdpi.com/2073-8994/2/2/609/pdf"}],"createdAt":"2010-04-07","modifiedAt":"2025-10-11","relatedProduct":[{"@id":"https://cir.nii.ac.jp/crid/1050845760781922176","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@language":"en","@value":"Effective field theory and the scattering process for magnons in ferromagnets, antiferromagnets, and ferrimagnets"}]},{"@id":"https://cir.nii.ac.jp/crid/1360002217836242560","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Unified Description of Nambu-Goldstone Bosons without Lorentz 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