The Mass Hyperboloid as a Poisson-Lie Group
High Energy Physics - Theory
2022-05-20 v1
Abstract
The light cone formalism of a massive scalar field has been shown by Dirac to have many advantages. But it is not manifestly Lorentz invariant. We will show that this is a feature not a bug: Lorentz invariance is indeed a symmetry, but in a different sense defined by Drinfel'd. The key idea is that the mass shell (mass hyperboloid) is a Poisson-Lie group: there is a non-abelian group multiplication and non-zero Poisson brackets between components of four-momentum. Rotations form the dual group of the hyperboloid in the sense of Drinfel'd. Infinitesimal Lorentz transformations form a Lie bi-algebra.
Cite
@article{arxiv.2205.09468,
title = {The Mass Hyperboloid as a Poisson-Lie Group},
author = {S. G. Rajeev and Patrizia Vitale},
journal= {arXiv preprint arXiv:2205.09468},
year = {2022}
}
Comments
9 pages. Latex file. Contribution dedicated to A. P. Balachandran, on the occasion of his eighty-fifth birthday