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ang-mills connections

Proceedings of the Edinburgh Mathematical Society (1)

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On a gauge-invariant functional
Part of
- Variational problems in infinite-dimensional spaces
Cătălin Gherghe
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 53 / Issue 1 / February 2010

Published online by Cambridge University Press:

12 January 2010, pp. 143-151
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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.