Abstract
The geometric quantization of a symplectic manifold endowed with a prequantum bundle and a metaplectic structure is defined by means of an integrable complex structure. We prove that its semi-classical limit does not depend on the choice of the complex structure. We show this in two ways. First, by introducing unitary identifications between the quantum spaces associated to the various complex polarizations and second, by defining an asymptotically flat connection in the bundle of quantum spaces over the space of complex structures. Furthermore Berezin-Toeplitz operators are intertwined by these identifications and have principal and subprincipal symbols defined independently of the complex structure. The relation with the Schrödinger equation and the group of prequantum bundle automorphisms is considered as well.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
