Geodesic
Quantisation of a Family of Phase Spaces
Informatics and Automation, Analysis and mathematical physics, Tome 311 (2020), pp. 250-263

Voir la notice de l'article provenant de la source Math-Net.Ru

We explain that when quantising phase spaces with varying symplectic structures, the bundle of quantum Hilbert spaces over the parameter space has a natural unitary connection. We then focus on symplectic vector spaces and their fermionic counterparts. After reviewing how the quantum Hilbert space depends on physical parameters such as the Hamiltonian and unphysical parameters such as choices of polarisations, we study the connection, curvature and phases of the Hilbert space bundle when the phase space structure itself varies. We apply the results to the $2$-sphere family of symplectic structures on a hyper-Kähler vector space and to their fermionic analogue, and conclude with possible generalisations. 
@article{TRSPY_2020_311_a14,
     author = {Siye Wu},
     title = {Quantisation of a {Family} of {Phase} {Spaces}},
     journal = {Informatics and Automation},
     pages = {250--263},
     publisher = {mathdoc},
     volume = {311},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2020_311_a14/}
}
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Siye Wu. Quantisation of a Family of Phase Spaces. Informatics and Automation, Analysis and mathematical physics, Tome 311 (2020), pp. 250-263. http://geodesic.mathdoc.fr/item/TRSPY_2020_311_a14/