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  02.06.2014 - Fractional Fourier Transform and Geometric Quantization-Seminario

Venerdi' 6 giugno, alle 16.00, presso l' aula seminari, il Prof. Kijowski terrà un seminario dal titolo:

Fractional Fourier Transform and Geometric Quantization

Abstract: Generalized Fourier transformation between the position and the momentum representation of a quantum state is constructed in a coordinate independent way. The only ingredient of this  construction is the symplectic (canonical) geometry of the phase-space: no linear structure is necessary. It is shown that the “fractional Fourier transform” provides a simple example of this construction. As an application of this techniques we show that for any linear Hamiltonian
system, its quantum dynamics can be obtained exactly as the lift of the corresponding classical dynamics
by means of the above transformation.
Moreover, it can be deduced from the free quantum evolution.  This way new, unknown symmetries of the Schrödinger equation can be constructed. It is also argued that the above construction defines in a natural way a connection in the bundle of quantum states, with the base space describing all their possible representations. The non-flatness of
this connection would be responsible for the non-existence of a quantum representation of the complete algebra of classical observables.