Journal of Lie Theory

no. 2
Fidelity and Metrics on Lorentz Boosts
Journal of Lie Theory, Volume 30 (2020) no. 2, pp. 445-459
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.
DOI: 10.5802/jolt.1124
Classification: 22E43, 20N05, 81P15
Keywords: Lorentz boost, Einstein gyrogroup, rapidity metric, Hilbert projective metric, fidelity, Wasserstein distance 
@article{JOLT_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},
     doi = {10.5802/jolt.1124},
     zbl = {1440.22026},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1124/}
}
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S. Kim. Fidelity and Metrics on Lorentz Boosts. Journal of Lie Theory, Volume 30 (2020) no. 2, pp. 445-459. doi: 10.5802/jolt.1124

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