Quantum description of angles in the plane

Authors

  • Roberto Beneduci Università della Calabria and Istituto Nazionale di Fisica Nucleare, Gruppo c. Cosenza, 87036 Arcavacata di Rende (Cs), Italy https://orcid.org/0000-0002-5838-1200
  • Emmanuel Frion University of Helsinki, Helsinki Institute of Physics, P. O. Box 64, FIN-00014 Helsinki, Finland https://orcid.org/0000-0003-1280-0315
  • Jean-Pierre Gazeau Université de Paris, CNRS, Astroparticule et Cosmologie, 75013 Paris, France

DOI:

https://doi.org/10.14311/AP.2022.62.0008

Keywords:

integral quantization, real Hilbert spaces, quantum entanglement

Abstract

The real plane with its set of orientations or angles in [0, π) is the simplest non trivial example of a (projective) Hilbert space and provides nice illustrations of quantum formalism. We present some of them, namely covariant integral quantization, linear polarisation of light as a quantum measurement, interpretation of entanglement leading to the violation of Bell inequalities, and spin one-half coherent states viewed as two entangled angles.

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References

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Published

2022-02-28

Issue

Vol. 62 No. 1 (2022): Analytic and Algebraic Methods in Physics

Section

Analytic and Algebraic Methods in Physics

License

Copyright (c) 2022 Roberto Beneduci, Emmanuel Frion, Jean-Pierre Gazeau

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Beneduci, R., Frion, E., & Gazeau, J.-P. (2022). Quantum description of angles in the plane. Acta Polytechnica, 62(1), 8-15. https://doi.org/10.14311/AP.2022.62.0008