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0801.53022
Gotay,
Mark J.
On symplectic submanifolds of cotangent bundles. (English)
[J] Lett.
Math. Phys. 29, No.4, 271-279 (1993). [ISSN 0377-9017]
Let $M$ be a differentiable manifold and $T\sp* M$ its canonical cotangent
bundle equipped with the standard symplectic form. Let $S$ be a symplectic
submanifold of $T\sp* M$. 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.
[ Z.Olszak
(Wroclaw) ]
Keywords: cotangent bundle; symplectic submanifold; Dirac manifolds