Gauge invariance and variational trivial problems on the bundle of connections.
| dc.contributor.author | Castrillón López, Marco | |
| dc.contributor.author | Muñoz Masqué, Jaime | |
| dc.contributor.author | Ratiu, T. | |
| dc.date.accessioned | 2023-06-20T10:38:21Z | |
| dc.date.available | 2023-06-20T10:38:21Z | |
| dc.date.issued | 2003-09 | |
| dc.description.abstract | Given a principal bundle P→M we classify all first order Lagrangian densities on the bundle of connections associated to P that are invariant under the Lie algebra of infinitesimal automorphisms. These are shown to be variationally trivial and to give constant actions that equal the characteristic numbers of P if dimM is even and zero if dimM is odd. In addition, we show that variationally trivial Lagrangians are characterized by the de Rham cohomology of the base manifold M and the characteristic classes of P of arbitrary degree | |
| dc.description.department | Depto. de Álgebra, Geometría y Topología | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/23326 | |
| dc.identifier.doi | 10.1016/S0926-2245(03)00016-0 | |
| dc.identifier.issn | 0926-2245 | |
| dc.identifier.officialurl | http://www.sciencedirect.com/science/article/pii/S0926224503000160 | |
| dc.identifier.relatedurl | http://www.sciencedirect.com/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/50861 | |
| dc.issue.number | 2 | |
| dc.journal.title | Differential Geometry and Its Applications | |
| dc.language.iso | eng | |
| dc.page.final | 145 | |
| dc.page.initial | 127 | |
| dc.publisher | Elsevier Science | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 514.7 | |
| dc.subject.keyword | Characteristic classes | |
| dc.subject.keyword | Connections on a principal bundle | |
| dc.subject.keyword | Euler–Lagrange equations | |
| dc.subject.keyword | Gauge invariance | |
| dc.subject.keyword | Infinitesimal symmetries | |
| dc.subject.keyword | Jet bundles | |
| dc.subject.keyword | Lagrangians | |
| dc.subject.keyword | Lie algebra representations | |
| dc.subject.keyword | Weil polynomials | |
| dc.subject.ucm | Geometría diferencial | |
| dc.subject.unesco | 1204.04 Geometría Diferencial | |
| dc.title | Gauge invariance and variational trivial problems on the bundle of connections. | |
| dc.type | journal article | |
| dc.volume.number | 19 | |
| dcterms.references | M.F. Atiyah, Complex analytic connections in fibre bundles, Trans. Amer. Math. Soc. 85 (1957) 181–207. M.F. Atiyah, L. Jeffrey, Topological Lagrangians and cohomology, J. Geom. Phys. 7 (1) (1990) 119–136. D.Bleecker, Gauge Theory and Variational Principles,Addison-Wesley, Reading, MA, 1981. A. Cabras, A.M. Vinogradov, Extensions of the Poisson bracket to differential forms and multi-vector fields, J. Geom. Phys. 9 (1992) 75–100. M. Castrillón López, J. Mu~noz Masqué, Gauge-invariant variationally trivial problems on T∗M, J. Math. Phys. 40 (1999) 821–829. J.L. Dupont, Curvature and Characteristic Classes, in: Lecture Notes in Math., Vol. 640, Springer-Verlag, New York, 1978. D.J. Eck, Gauge-natural bundles and generalized gauge theories, Mem. Amer. Math. Soc. 247 (1981). P.L. García, Connections and 1-jet bundles, Rend. Sem. Mat. Univ. Padova 47 (1972) 227–242. P.L. García, Gauge algebras, curvature and symplectic structure, J. Differential Geom. 12 (1977) 209–227. P.B. Gilkey, Invariance Theory, the Heat Equation, and the Atiyah-Singer Index Theorem, CRC Press, Boca Raton, 1995. V. Guillemin, S. Sternberg, Symplectic Techniques in Physics, Cambridge University Press, Cambridge, UK, 1983. D. Husemoller, Fibre Bundles, 3rd Edition, Springer-Verlag, New York, 1994. S. Kobayashi, K. Nomizu, Foundations of Differential Geometry, Vol. I, Wiley-Interscience, New York, 1963; Vol. II, 1969. I. Kolář, P.W. Michor, J. Slovák, Natural Operations in Differential Geometry, Springer-Verlag, Berlin, 1993. D. Krupka, Of the structure of the Euler mapping, Arch. Math. 1, Scripta Fac. Sci. Nat. UJEP Brunensis 10 (1974) 55–62. D. Krupka, Trivial Lagrangians in field theory, Differential Geom. Appl. 9 (1998) 293–305. Y.I. Manin, Frobenius Manifolds, Quantum Cohomology, and Moduli Spaces, in: Colloquium Publications, Vol. 47, American Mathematical Society, Providence, RI, 1999. J.W. Milnor, J.D. Stasheff, Characteristic Classes, in: Ann. Math. Stud., Vol. 76, Princeton University Press, Princeton, 1974. D.J. Saunders, The Geometry of Jet Bundles, Cambridge University Press, Cambridge, UK, 1989. R. Utiyama, Invariant theoretical interpretation of interaction, Phys. Rev. 101 (1956) 1597–1607. | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 32e59067-ef83-4ca6-8435-cd0721eb706b | |
| relation.isAuthorOfPublication.latestForDiscovery | 32e59067-ef83-4ca6-8435-cd0721eb706b |
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