Dependence of the affine coherent states quantization on the parametrization of the affine group
Institute of Physics, Maria Curie-Skłodowska University, pl. Marii Curie-Skłodowskiej 1, 20-031, Lublin, Poland
2 Department of Fundamental Research, National Centre for Nuclear Research, Pasteura 7, 02-093, Warszawa, Poland
3 Institut für Theoretische Physik, Universität zu Köln, Zülpicher Straße 77, 50937, Köln, Germany
Accepted: 8 December 2020
Published online: 2 January 2021
The affine coherent states quantization is a promising integral quantization of Hamiltonian systems when the phase space includes at least one conjugate pair of variables which takes values from a half plane. Such a situation is common for gravitational systems which include singularities. The construction of the quantization map includes a one-to-one mapping of the half plane onto the affine group. Particular cases of this mapping define specific parametrizations of the group. Our aim is showing that different such parametrizations lead to unitarily inequivalent quantum theories. Depending on the Hamiltonian system under consideration, this dependence could potentially be used constructively.
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