https://doi.org/10.1140/epjc/s10052-025-14254-2
Regular Article - Theoretical Physics
Integral quantization based on the Heisenberg–Weyl group
1
Department of Fundamental Research, National Centre for Nuclear Research, Pasteura 7, 02-093, Warsaw, Poland
2
Institute of Physics, Maria Curie-Skłodowska University, pl. Marii Curie-Skłodowskiej 1, 20-031, Lublin, Poland
3
Institute of Theoretical Physics, Jagiellonian University, Łojasiewicza 11, 30-348, Kraków, Poland
a
wlodzimierz.piechocki@ncbj.gov.pl
Received:
13
March
2025
Accepted:
29
April
2025
Published online:
4
June
2025
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. 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.
© The Author(s) 2025
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