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Hamiltonian symplectomorphisms and the Berry phase

✍ Scribed by Andrés Viña

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
183 KB
Volume
40
Category
Article
ISSN
0393-0440

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✦ Synopsis

On the space L, of loops in the group of Hamiltonian symplectomorphisms of a symplectic quantizable 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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