Date: Friday, October 22, 2021 | 10:00 (GMT+1) (Virtual)
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Prof. Jean Pierre Gazeau | Professeur émérite, Université Paris Diderot, Paris, France
TITLE:
Real POVMS on the plane: integral quantization, Naimark theorem and linear polarization of the light.
ABSTRACT:
I will introduce and discuss some of the most basic fundamental concepts of quantum physics by using orientations or angles in the plane, illustrated through linear polarisations of the light and the associated Stokes parameters. Starting with the Euclidean plane, which is certainly a paradigmatic example of a Hilbert space, the orientations in the plane are identified with the pure states.
Associating these quantum orientations with linear polarisations of light in the plane normal to its propagation constitutes an immediate and nice illustration of the presented formalism. Another contribution concerns the description of the dynamics of quantum states. The pure states form the unit circle (actually a half of it) and the mixed states form the unit disk (actually a half of it). Rotations in the plane rule time evolution through Majorana-like equations involving only real quantities for closed (Heisenberg-Dirac) and open (Lindblad) systems. Interesting probabilistic aspects are developed. Finally, I revisit light linear polarisation as an example of quantum measurement through Stokes parameters.