Hamiltonian monodromy via geometric quantization in completely integrable Hamiltonian systems.
Expositor: Nicola Sansonetto
Instituição: Univ. de Verona
Data e Horário: 08/06/18 | 14:00h

RESUMO: Hamiltonian monodromy is addressed from the point of view of geometric quantization, and various differential geometric aspects thereof are dealt with, all related to holonomies of suitable flat connections.
In the case of completely integrable Hamiltonian systems with two degrees of freedom, a link is established between monodromy and (two-level) theta functions, by resorting to the by now classical differential
geometric interpretation of the latter as covariantly constant sections of a flat connection, via the heat equation. Finally, a new derivation of the monodromy of the spherical pendulum is provided.

[SS] N. Sansonetto and M. Spera, Hamiltonian monodromy via geometric quantization and theta functions. J. Geom. Phys. 60 (2010), 501–512.

[S] N. Sansonetto, Monodromy and Bohr—Sommerfeld geometric quantization. J. Geom. and Symm. Phys.  20 (2010), 97–106