Elementary Proof of Moretti's Polar Decomposition Theorem for Lorentz Transformations

TL;DR

This paper provides a simpler, more elementary proof of Moretti's theorem, showing that the polar decomposition of Lorentz matrices corresponds to their standard rotation-boost decomposition.

Contribution

It introduces an elementary proof of Moretti's Lorentz matrix decomposition, simplifying the understanding of the theorem compared to the original proof.

Findings

Polar decomposition of Lorentz matrices equals standard rotation-boost decomposition

Elementary proof simplifies understanding of Lorentz matrix decompositions

Confirms the analogy with the complex SL(2,C) case

Abstract

A proof more elementary than the original one is given for Moretti's theorem that the usual polar decomposition of real matrices when applied to an orthochronous proper Lorentz matrix yields just its standard rotation-boost decomposition. (The complex SL(2,C) analog is well-known.)