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Castrillón López, Marco
(1999)
*Gauge invariant variationally trivial U(1)-problems.*
In
Differential geometry and applications.
Masaryk University, Brno, pp. 461-468.
ISBN 80-210-2097-0

Official URL: http://cisne.sim.ucm.es/record=b1962340~S6*spi

## Abstract

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 χ on the ground manifold M which are divergence-free, that is, Lχv=0, v being a fixed volume form on M.

Item Type: | Book Section |
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Additional Information: | Proceedings of the 7th International Conference (DGA98) held in Brno, August 10–14, 1998. |

Subjects: | Sciences > Mathematics > Differential equations |

ID Code: | 24317 |

Deposited On: | 22 Jan 2014 18:10 |

Last Modified: | 12 Dec 2018 15:13 |

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