dc.contributor.author Batlle Arnau, Carles dc.contributor.author Gomis Torné, Joaquin dc.contributor.author Ray, Sourya dc.contributor.author Zanelli, Jorge dc.contributor.other Universitat Politècnica de Catalunya. Departament de Matemàtiques dc.date.accessioned 2019-04-12T08:17:06Z dc.date.available 2019-04-12T08:17:06Z dc.date.issued 2019-03-15 dc.identifier.citation Batlle, 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.issn 2470-0010 dc.identifier.other https://arxiv.org/pdf/1812.05837.pdf dc.identifier.uri http://hdl.handle.net/2117/131698 dc.description.abstract We 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.extent 12 p. dc.language.iso eng dc.publisher American Physical Society (APS) dc.rights Attribution-NonCommercial-NoDerivs 3.0 Spain dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/3.0/es/ dc.subject Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra dc.subject.lcsh Symmetry dc.subject.lcsh Lie algebras dc.title Lie symmetries of nonrelativistic and relativistic motions dc.type Article dc.subject.lemac Simetria (Física) dc.subject.lemac Simetria dc.subject.lemac Lie, Àlgebres de dc.contributor.group Universitat Politècnica de Catalunya. ACES - Control Avançat de Sistemes d'Energia dc.identifier.doi 10.1103/PhysRevD.99.064015 dc.description.peerreviewed Peer Reviewed dc.relation.publisherversion https://journals.aps.org/prd/abstract/10.1103/PhysRevD.99.064015 dc.rights.access Open Access drac.iddocument 24243801 dc.description.version Postprint (published version) upcommons.citation.author Batlle, C.; Gomis, J.; Ray, S.; Zanelli, J. upcommons.citation.published true upcommons.citation.publicationName Physical review D upcommons.citation.volume 99 upcommons.citation.number 6 upcommons.citation.startingPage 1 upcommons.citation.endingPage 12
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