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On a gauge-invariant functional

Part of: Variational problems in infinite-dimensional spaces

Published online by Cambridge University Press:  12 January 2010

Cătălin Gherghe
Cătălin Gherghe
Affiliation:
Faculty of Mathematics, University of Bucharest, Academiei 14, 010014 Bucharest, Romania, Email: ([email protected])
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Abstract

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We define a new functional which is gauge invariant on the space of all smooth connections of a vector bundle over a compact Riemannian manifold. This functional is a generalization of the classical Yang-Mills functional. We derive its first variation formula and prove the existence of critical points. We also obtain the second variation formula.

Keywords

curvaturevector bundleang-Mills connections

MSC classification

Secondary: 58E15: Application to extremal problems in several variables; Yang-Mills functionals , etc.
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 53 , Issue 1 , February 2010 , pp. 143 - 151
Copyright
Copyright © Edinburgh Mathematical Society 2010