| Título: | Gauge invariance on principal SU(2)-bundles |
| Autores: | Castrillón López, Marco ; Muñoz Masqué, Jaime |
| Tipo de documento: | texto impreso |
| Editorial: | American Mathematical Society, 1998 |
| Dimensiones: | application/pdf |
| Nota general: | info:eu-repo/semantics/openAccess |
| Idiomas: | |
| Palabras clave: | Estado = Publicado , Materia = Ciencias: Matemáticas: Geometría diferencial , Tipo = Sección de libro |
| Resumen: |
Let ?:P?M be a principal G-bundle. One denotes by J1P the 1-jet bundle of local sections of ?, by autP the Lie algebra of G-invariant vector fields of P and by gauP the ideal of ?-vertical vector fields in autP. A differential form ? on J1P is said to be autP-invariant [resp. gauP-invariant] if LX(1)?=0 for every X?autP [resp. X?gauP], where X(1) is the natural lift of X?X(P) to J1P, i.e., X(1) is the infinitesimal contact transformation associated to X. The authors of the present paper study the structure of autP- and gau P-invariant forms, when the structure group is G=SU(2). They prove that the algebra of autP-invariant [resp. gauP-invariant] forms is differentiably generated over the real numbers [resp. over the graded algebra of differential forms on M] by the standard structure forms. These are the 1-forms ?a obtained when one decomposes the standard su(2)-valued 1-form ? on J1P as ?=?a?Ba, a?{1,2,3}, where Ba is the standard basis of the Lie algebra su(2). On the other hand, by means of the identification between the affine bundle C(P)?M of connections on P and the quotient bundle (J1P)/G?M, they show that the representation autP?X(C(P)) can be obtained by infinitesimal contact transformations |
| En línea: | https://eprints.ucm.es/id/eprint/24330/1/castrill%C3%B3n280.pdf |
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