Looking for Carroll Particles in the Two-Time Spacetime

Authors

  • A. Kamenshchik Dipartimento di Fisica e Astronomia, Universit`a di Bologna, I.N.F.N., Sezione di Bologna
  • F. Muscolino Department of Science and High Technology, Universit`a dell’Insubria, I.N.F.N., Sezione di Milano

DOI:

https://doi.org/10.15407/ujpe69.7.448

Keywords:

two-time spacetime, Carroll group, particles

Abstract

We make an attempt to describe Carroll particles with a non-vanishing value of energy (i.e., the Carroll particles which always stay in rest) in the framework of two-time physics, developed in the series of papers by I. Bars and his co-authors. In the spacetime with one additional time dimension and one additional space dimension, where one can localize the symmetry which exists between generalized coordinates and their conjugate momenta. Such a localization implies the introduction of the gauge fields, which, in turn, implies the appearance of some first-class constraints. Choosing different gauge-fixing conditions and solving the constraints, we obtain different time parameters, Hamiltonians, and, generally, physical systems in the standard one-time spacetime. We find a set of gauge fixing conditions which gives the description of a Carroll particle in the one-time world. We construct the quantum theory of such a particle using an unexpected correspondence between our parametrization and that obtained by Bars for the hydrogen atom in 1999.

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Published

2024-08-27

How to Cite

Kamenshchik, A., & Muscolino, F. (2024). Looking for Carroll Particles in the Two-Time Spacetime. Ukrainian Journal of Physics, 69(7), 448. https://doi.org/10.15407/ujpe69.7.448

Issue

Section

Non-Euclidean Geometry in Modern Physics and Mathematics