Abstract
The cotangent bundle of a manifold M can be identified with the bundle of connections of the trivial bundle M×U(1). Hence, there exists a natural representation of the U(1)-invariant vector fields on M×U(1) extending the gauge representation into the Lie algebra of vector fields on T*(M). It is proved herein that a differential form on T*(M) is invariant under this representation (resp. gauge invariant) if and only if it belongs to the R-algebra [resp. to the Ω ̇ (M)-algebra] generated by the canonical symplectic form of the cotangent bundle.
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