Hamiltonian structure of gauge-invariant variational problems
| dc.contributor.author | Castrillón López, Marco | |
| dc.contributor.author | Muñoz Masqué, Jaime | |
| dc.date.accessioned | 2023-06-20T03:36:04Z | |
| dc.date.available | 2023-06-20T03:36:04Z | |
| dc.date.issued | 2012 | |
| dc.description.abstract | Let C→M be the bundle of connections of a principal bundle on M . The solutions to Hamilton–Cartan equations for a gauge-invariant Lagrangian density Λ on C satisfying a weak condition of regularity, are shown to admit an affine fibre-bundle structure over the set of solutions to Euler–Lagrange equations for Λ . This structure is also studied for the Jacobi fields and for the moduli space of extremals. | |
| dc.description.department | Depto. de Álgebra, Geometría y Topología | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.faculty | Instituto de Matemática Interdisciplinar (IMI) | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | Ministerio de Ciencia e Innovación | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/23104 | |
| dc.identifier.doi | 10.4310/ATMP.2012.v16.n1.a2 | |
| dc.identifier.issn | 1095-0761 | |
| dc.identifier.officialurl | http://intlpress.com/site/pub/pages/journals/items/atmp/content/vols/0016/0001/a002/index.html | |
| dc.identifier.relatedurl | http://intlpress.com/site/_home/index.html | |
| dc.identifier.relatedurl | http://arxiv.org/pdf/1004.4923.pdf | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/44008 | |
| dc.issue.number | 1 | |
| dc.journal.title | Advances in Theoretical and Mathematical Physics | |
| dc.language.iso | spa | |
| dc.page.final | 63 | |
| dc.page.initial | 39 | |
| dc.publisher | International Press | |
| dc.relation.projectID | MTM2008–01386 | |
| dc.relation.projectID | MTM2007–60017 | |
| dc.rights.accessRights | open access | |
| dc.subject.cdu | 514.7 | |
| dc.subject.keyword | Bundle of connections | |
| dc.subject.keyword | Gauge invariance | |
| dc.subject.keyword | Hamilton-Cartan equations | |
| dc.subject.keyword | Jacobi field | |
| dc.subject.keyword | Jet bundles | |
| dc.subject.keyword | Euler-Lagrange equations | |
| dc.subject.keyword | Poincaré-Cartan form | |
| dc.subject.ucm | Geometría diferencial | |
| dc.subject.unesco | 1204.04 Geometría Diferencial | |
| dc.title | Hamiltonian structure of gauge-invariant variational problems | |
| dc.type | journal article | |
| dc.volume.number | 16 | |
| dcterms.references | D. Bleecker, Gauge theory and variational principles, Global Analysis Pure and Applied Series A, 1, Addison-Wesley Publishing Co., Reading, MA, 1981. M. Castrillón López and J. Muñoz Masqué, The geometry of the bundle of connections, Math. Z. 236 (2001), 797–811. M. Castrillón López and J. Muñoz Masqué, Independence of Yang–Mil ls equations with respect to the invariant pairing in the Lie algebra, Int. J. Theor. Phys. 46(4) (2007), 1020–1026. M. Castrillón López and J. Muñoz Masqué, Gauge-invariant characterization of Yang–Mills–Higgs equations, Ann. Henri Poincaré 8 (2007), 203–217. M. Castrillón López, J. Muñoz Masqué and T. Ratiu, Gauge invariance and variational trivial problems on the bundle of connections, Differ. Geom. Appl. 19(2) (2003), 127–145. P. Cotta-Ramusino and C. Reina, The action of the group of bundle- automorphisms on the space of connections and the geometry of gauge theories, J. Geom. Phys. 1(3) (1984), 121–155. P.L. García Pérez, The Poincaré–Cartan invariant in the calculus of variations, Symposia Mathematica, Volume XIV (Convegno di Geometria Simplettica e Fisica Matematica, INDAM, Rome, 1973), London, Academic Press, 1974, 219–246. H. Goldschmidt and S. Sternberg, The Hamilton–Cartan formalism in the calculus of variations, Ann. Inst. Fourier (Grenoble) 23 (1973), 203–267. J. Jost, X. Peng and G. Wang, Variational aspects of the Seiberg-Witten functional, Calc. Var. Partial Differ. Equ. 4(3) (1996), 205–218. S. Kobayashi and K. Nomizu, Foundations of Differential Geometry, New York, John Wiley & Sons, Inc. (Interscience Division), Vol I, 1963. L. Lemaire and J.C. Wood, Jacobi fields along harmonic 2-spheres in CP 2 are integrable, J. Lond. Math. Soc. (2) 66(2) (2002), 468–486. F. Lin and Ch. Wang, The analysis of harmonics maps and their heat lows, Singapore, World Scientific Publishing Co. Pte. Ltd., 2008. P.K. Mitter and C.M. Viallet, On the bundle of connections and the gauge orbit manifold in Yang–Mills theory, Comm. Math. Phys. 79(4) (1981), 457–472. J. Muñoz Masqué and L.M. Pozo Coronado, Parameter invariance in field theory and the Hamiltonian formalism, Fortschr. Phys. 48 (2000), 361–405. Y. Okawa, Derivative corrections to Dirac-Born-Infeld Lagrangian and non-commutative gauge theory, Nucl. Phys. B 566(1–2) (2000), 348–362. T. Suzuki, Born-Infeld action in (n +2)-dimension, the field equation and a soliton solution, Lett. Math. Phys. 47(2) (1999), 159–171. | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 32e59067-ef83-4ca6-8435-cd0721eb706b | |
| relation.isAuthorOfPublication.latestForDiscovery | 32e59067-ef83-4ca6-8435-cd0721eb706b |
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