Título: | Gauge invariant variationally trivial U(1)-problems. |
Autores: | Castrillón López, Marco |
Tipo de documento: | texto impreso |
Editorial: | Masaryk University, 1999 |
Palabras clave: | Estado = Publicado , Materia = Ciencias: Matemáticas: Ecuaciones diferenciales , Tipo = Sección de libro |
Resumen: |
One of the classical problems in the theory of variational calculus is the so-called equivalence problem, which studies whether two Lagrangians L, L?, defined in the 1-jet prolongation of a given bundle, determine the same variational problem. This problem is equivalent to studying the variational triviality of the difference L?L?. On the other hand, the notion of gauge invariance plays a relevant role in the theory of fields, in particular in electromagnetism, in which the structure group is the abelian group U(1). In this framework, the author gives a geometric characterization of the trivial variational problems defined on the bundle of connections of an arbitrary U(1)-principal bundle which are gauge-invariant. It turns out that there is a one-to-one correspondence between the set of these problems and the set of multivector fields ? on the ground manifold M which are divergence-free, that is, L?v=0, v being a fixed volume form on M. |
Ejemplares
Estado |
---|
ningún ejemplar |