| Título: | Gauge interpretation of characteristic classes |
| Autores: | Castrillón López, Marco ; Muñoz Masqué, Jaime |
| Tipo de documento: | texto impreso |
| Editorial: | International Press, 2001 |
| Dimensiones: | application/pdf |
| Nota general: | info:eu-repo/semantics/openAccess |
| Idiomas: | |
| Palabras clave: | Estado = Publicado , Materia = Ciencias: Matemáticas: Geometría diferencial , Tipo = Artículo |
| Resumen: |
Let ?:P?M be a principal G-bundle. Then one can consider the following diagram of fibre bundles: \CD J^{1}(P) @>\pi_{10}>> P\\ @VqVV @VV\pi V\\ C(P) @>p>> M\endCD where p is the bundle of connections of ?. As is well known, q is also a principal G-bundle, and the canonical contact form ? on J1(P) can be considered as a connection form on q, with curvature form ?. One defines aut P as the Lie algebra of G-invariant vector fields on P and gau P as the ideal of ?-vertical G-invariant vector fields on P. If X?autP?X(P), then one defines the infinitesimal contact transformation associated to X, X1?X(J1(P)), and its q-projection XC?X(C(P)). A differential form ? on C(P) is said to be aut P-invariant [resp. gauge invariant] if LXC?=0 for every X?autP [resp. X?gauP]. On the other hand, let us denote by g the Lie algebra of G. An element of the symmetric algebra of g? will be called a Weil polynomial. The main result of the paper is the following theorem: If G is connected, for every gauge invariant form ? on C(P) there exist differential forms ?1,…,?k on M and Weil polynomials f1,…,fk such that ?=p?(?1)?f1(?)+?+p?(?k)?fk(?). As a consequence, the authors prove that a differential form ? on C(P) is aut P-invariant iff ?=f(?), where f is a Weil polynomial, and then ? is closed. Explicit examples are shown and the link between the above theorem and the geometric formulation of Utiyama's theorem is explained. |
| En línea: | https://eprints.ucm.es/id/eprint/24200/1/castrill%C3%B3n200pdf.pdf |
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