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
- License:
- 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.
Related papers
Err
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.