Geodesic
Fidelity and Metrics on Lorentz Boosts
Journal of Lie theory, Tome 30 (2020) no. 2, pp. 445-459
Cet article a éte moissonné depuis la source Heldermann Verlag

Voir la notice de l'article

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 
@article{JLT_2020_30_2_JLT_2020_30_2_a8,
     author = {S. 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/JLT_2020_30_2_JLT_2020_30_2_a8/}
}
TY  - JOUR
AU  - S. Kim
TI  - Fidelity and Metrics on Lorentz Boosts
JO  - Journal of Lie theory
PY  - 2020
SP  - 445
EP  - 459
VL  - 30
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/JLT_2020_30_2_JLT_2020_30_2_a8/
ID  - JLT_2020_30_2_JLT_2020_30_2_a8
ER  - 
%0 Journal Article
%A S. Kim
%T Fidelity and Metrics on Lorentz Boosts
%J Journal of Lie theory
%D 2020
%P 445-459
%V 30
%N 2
%U http://geodesic.mathdoc.fr/item/JLT_2020_30_2_JLT_2020_30_2_a8/
%F JLT_2020_30_2_JLT_2020_30_2_a8
S. Kim. Fidelity and Metrics on Lorentz Boosts. Journal of Lie theory, Tome 30 (2020) no. 2, pp. 445-459. http://geodesic.mathdoc.fr/item/JLT_2020_30_2_JLT_2020_30_2_a8/