Fidelity and Metrics on Lorentz Boosts
Journal of Lie Theory, Tome 30 (2020) no. 2, pp. 445-459
Voir la notice de l'article provenant de la source Heldermann Verlag
We see in this article that the extended version of a real counterpart of qubit density matrices introduced by Abraham Ungar, called a Moebius matrix, is indeed a normalized Lorentz boost by finding its spectral decomposition. Using the gyrogroup isomorphism between the set of all Lorentz boosts and the Einstein gyrogroup on the open unit ball of the n-dimensional Euclidean space, we give a gyrogroup structure on the set of Lorentz boosts and compute various metric formulas of Lorentz boosts such as the Riemannian trace metric, Hilbert projective metric, fidelity and Wasserstein distance in terms of Lorentz gamma factors.
Classification :
22E43, 20N05, 81P15
Mots-clés : Lorentz boost, Einstein gyrogroup, rapidity metric, Hilbert projective metric, fidelity, Wasserstein distance
Mots-clés : Lorentz boost, Einstein gyrogroup, rapidity metric, Hilbert projective metric, fidelity, Wasserstein distance
Affiliations des auteurs :
Sejong Kim 1
Sejong Kim. Fidelity and Metrics on Lorentz Boosts. Journal of Lie Theory, Tome 30 (2020) no. 2, pp. 445-459. http://geodesic.mathdoc.fr/item/JOLT_2020_30_2_a8/
@article{JOLT_2020_30_2_a8,
author = {Sejong Kim},
title = {Fidelity and {Metrics} on {Lorentz} {Boosts}},
journal = {Journal of Lie Theory},
pages = {445--459},
year = {2020},
volume = {30},
number = {2},
url = {http://geodesic.mathdoc.fr/item/JOLT_2020_30_2_a8/}
}