Integral quantization based on the Heisenberg-Weyl group

• URL: http://arxiv.org/abs/2410.23982v1
• Date: Thu, 31 Oct 2024 14:36:38 GMT
• Title: Integral quantization based on the Heisenberg-Weyl group
• Authors: Aleksandra Pȩdrak, Andrzej Góźdź, Włodzimierz Piechocki, Patryk Mach, Adam Cieślik,
• Abstract summary: We develop a framework of integral quantization applied to the motion of spinless particles in the four-dimensional Minkowski spacetime. The proposed scheme is based on coherent states generated by the action of the Heisenberg-Weyl group. A direct application of our model, including a computation of transition amplitudes between states characterized by fixed positions and momenta, is postponed to a forthcoming article.
• Score: 39.58317527488534
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• Abstract: We develop a relativistic framework of integral quantization applied to the motion of spinless particles in the four-dimensional Minkowski spacetime. The proposed scheme is based on coherent states generated by the action of the Heisenberg-Weyl group and has been motivated by the Hamiltonian description of the geodesic motion in General Relativity. We believe that this formulation should also allow for a generalization to the motion of test particles in curved spacetimes. A key element in our construction is the use of suitably defined positive operator-valued measures. We show that this approach can be used to quantize the one-dimensional nonrelativistic harmonic oscillator, recovering the standard Hamiltonian as obtained by the canonical quantization. Our formalism is then applied to the Hamiltonian associated with the motion of a relativistic particle in the Minkowski spacetime. A direct application of our model, including a computation of transition amplitudes between states characterized by fixed positions and momenta, is postponed to a forthcoming article.

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