English

Quantization in Cartesian coordinates and the Hofer metric

Mathematical Physics 2022-04-06 v2 General Relativity and Quantum Cosmology High Energy Physics - Theory math.MP Classical Physics Quantum Physics

Abstract

P.A.M. Dirac had stated that the Cartesian coordinates are uniquely suited for expressing the canonical commutation relations in a simple form. By contrast, expressing these commutation relations in any other coordinate system is more complicated and less obvious. The question that we address in this work, is the reason why this is true. We claim that this unique role of the Cartesian coordinates is a result of the existence and uniqueness of the Hofer metric on the space of canonical transformations of the phase space of the system getting quantized.

Keywords

Cite

@article{arxiv.2111.14350,
  title  = {Quantization in Cartesian coordinates and the Hofer metric},
  author = {Nikolaos Kalogeropoulos and Christos Kokorelis},
  journal= {arXiv preprint arXiv:2111.14350},
  year   = {2022}
}

Comments

22 pages, No figures, LaTeX2e, Very minor corrections on this version

R2 v1 2026-06-24T07:55:15.394Z