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Gauge invariance and variational trivial problems on the bundle of connections.

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Castrillón López, Marco and Muñoz Masqué, Jaime and Ratiu, T. (2003) Gauge invariance and variational trivial problems on the bundle of connections. Differential Geometry and Its Applications, 19 (2). pp. 127-145. ISSN 0926-2245

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Official URL: http://www.sciencedirect.com/science/article/pii/S0926224503000160


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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


Item Type:Article
Uncontrolled Keywords:Characteristic classes; Connections on a principal bundle; Euler–Lagrange equations; Gauge invariance; Infinitesimal symmetries; Jet bundles; Lagrangians; Lie algebra representations; Weil polynomials
Subjects:Sciences > Mathematics > Differential geometry
ID Code:23326
Deposited On:22 Oct 2013 17:39
Last Modified:12 Dec 2018 15:13

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