Quantisation of the cotangent bundle of Lie groups
Starts 17 May 2013 16:00
Ends 17 May 2013 20:00
Central European Time
Leonardo da Vinci Building Luigi Stasi Seminar Room
Strada Costiera, 11
I - 34151 Trieste (Italy)
We consider a family of adapted complex structures on the cotangent bundle of a Lie group and find the BKS pairing relating the corresponding half-form quantisation. We show that the resulting bundle of quantum Hilbert spaces over the space of polarisations is flat. The vertical polarisation as a limit of complex polarisations yields the coherent state transform (or the Segal-Bargmann-Hall transform). We show that there is another limit of the complex polarisations that corresponds to the Peter-Weyl theorem.
This is a joint work with W. Kirwin.