On symplectic submanifolds of cotangent bundles
Let \(M\) be a differentiable manifold and \(T^* M\) its canonical cotangent bundle equipped with the standard symplectic form. Let \(S\) be a symplectic submanifold of \(T^* M\). The author derives analytic, necessary and sufficient conditions for \(S\) to be the canonical cotangent bundle of a submanifold of \(M\) or, more generally, of a quotient space of a submanifold of \(M\). Next, he discusses several physical examples of his results. Especially, massive scalar particles, fixed-point sets of symplectic group actions, Dirac manifolds for angular momentum, the Proca field.
scientific article; zbMATH DE number 508689