0 Hamiltonian Symplectomorphisms and the Berry Phase
نویسنده
چکیده
On the space L, of loops in the group of Hamiltonian symplecto-morphisms of a symplectic manifold, we define a closed Z-valued 1-form Ω. If Ω vanishes, the prequantization map can be extended to a group representation. On L one can define an action integral as an R/Z-valued function, and the cohomology class [Ω] is the obstruction to the lifting of that action integral to an R-valued function. The form Ω also defines a natural grading on π 1 (L).
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