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dc.contributor.authorBatlle Arnau, Carles
dc.contributor.authorGomis Torné, Joaquin
dc.contributor.authorRay, Sourya
dc.contributor.authorZanelli, Jorge
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtiques
dc.date.accessioned2019-04-12T08:17:06Z
dc.date.available2019-04-12T08:17:06Z
dc.date.issued2019-03-15
dc.identifier.citationBatlle, C. [et al.]. Lie symmetries of nonrelativistic and relativistic motions. "Physical review D", 15 Març 2019, vol. 99, núm. 6, p. 1-12.
dc.identifier.issn2470-0010
dc.identifier.otherhttps://arxiv.org/pdf/1812.05837.pdf
dc.identifier.urihttp://hdl.handle.net/2117/131698
dc.description.abstractWe study the Lie symmetries of non-relativistic and relativistic higher order constant motions in d spatial dimensions, i.e. constant acceleration, constant rate-of-change -of-acceleration (constant jerk), and so on. In the non-relativistic case, these symmetries contain the z =2 N Galilean conformal transformations, where N is the order of the differential equation that defines the constant motion. The dimension of this group grows with N. In the relativistic case the vanishing of the (d+1)-dimensional space-time relativistic acceleration, jerk, snap, . . . , is equivalent, in each case, to the vanishing of a d-dimensional spatial vector. These vectors are the d-dimensional non-relativistic ones plus additional terms that guarantee the relativistic transformation properties of the corresponding d + 1 dimensional vectors. In the case of acceleration there are no corrections, which implies that the Lie symmetries of zero acceleration motions are the same in the non-relativistic and relativistic cases. The number of Lie symmetries that are obtained in the relativistic case does not increase from the four-derivative order (zero relativistic snap) onwards. We also deduce a recurrence relation for the spatial vectors that in the relativistic case characterize the constant motions
dc.format.extent12 p.
dc.language.isoeng
dc.publisherAmerican Physical Society (APS)
dc.rightsAttribution-NonCommercial-NoDerivs 3.0 Spain
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra
dc.subject.lcshSymmetry
dc.subject.lcshLie algebras
dc.titleLie symmetries of nonrelativistic and relativistic motions
dc.typeArticle
dc.subject.lemacSimetria (Física)
dc.subject.lemacSimetria
dc.subject.lemacLie, Àlgebres de
dc.contributor.groupUniversitat Politècnica de Catalunya. ACES - Control Avançat de Sistemes d'Energia
dc.identifier.doi10.1103/PhysRevD.99.064015
dc.description.peerreviewedPeer Reviewed
dc.relation.publisherversionhttps://journals.aps.org/prd/abstract/10.1103/PhysRevD.99.064015
dc.rights.accessOpen Access
drac.iddocument24243801
dc.description.versionPostprint (published version)
upcommons.citation.authorBatlle, C.; Gomis, J.; Ray, S.; Zanelli, J.
upcommons.citation.publishedtrue
upcommons.citation.publicationNamePhysical review D
upcommons.citation.volume99
upcommons.citation.number6
upcommons.citation.startingPage1
upcommons.citation.endingPage12


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