The interplay of the polar decomposition theorem and the Lorentz group

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dc.creatorMoretti, Valter
dc.date2002-11-20
dc.date.accessioned2026-07-07T04:29:35Z
dc.date.available2026-07-07T04:29:35Z
dc.descriptionIt is shown that the polar decomposition theorem of operators in (real) Hilbert spaces gives rise to the known decomposition in boost and spatial rotation part of any matrix of the orthochronous proper Lorentz group $SO(1,3)\uparrow$. This result is not trivial because the polar decomposition theorem is referred to a positive defined scalar product while the Lorentz-group decomposition theorem deals with the indefinite Lorentz metric. A generalization to infinite dimensional spaces can be given. It is finally shown that the polar decomposition of $SL(2,\bC)$ is preserved by the covering homomorphism of $SL(2,\bC)$ onto $SO(1,3)\spa\uparrow$
dc.description7 pages, no figures, LaTeX 2e
dc.identifierhttps://arxiv.org/abs/math-ph/0211047
dc.identifierhttp://arxiv.org/abs/math-ph/0211047
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/57212
dc.subjectMathematical Physics
dc.subjectGeneral Relativity and Quantum Cosmology
dc.subjectGroup Theory
dc.titleThe interplay of the polar decomposition theorem and the Lorentz group
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