About Chirality in Minkowski Spacetime

In this paper, we show that Lorentz boosts are direct isometries according to the recent mathematical definitions of direct and indirect isometries and of chirality, working for any metric space. Here, these definitions are extended to the Minkowski spacetime. We also show that the composition of pa...

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Main Author:	Michel Petitjean
Format:	Article
Language:	English
Published:	MDPI AG 2019-10-01
Series:	Symmetry
Subjects:	chirality definition symmetry mikowski spacetime isometries
Online Access:	https://www.mdpi.com/2073-8994/11/10/1320

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spelling	doaj-716edb9384a349ddba9ccbdea92503fd2020-11-25T01:56:45ZengMDPI AGSymmetry2073-89942019-10-011110132010.3390/sym11101320sym11101320About Chirality in Minkowski SpacetimeMichel Petitjean0Université de Paris, BFA, CNRS UMR 8251, INSERM ERL U1133, 75013 Paris, FranceIn this paper, we show that Lorentz boosts are direct isometries according to the recent mathematical definitions of direct and indirect isometries and of chirality, working for any metric space. Here, these definitions are extended to the Minkowski spacetime. We also show that the composition of parity inversion and time reversal is an indirect isometry, which is the opposite of what could be expected in Euclidean spaces. It is expected that the extended mathematical definition of chirality presented here can contribute to the unification of several definitions of chirality in space and in spacetime, and that it helps clarify the ubiquitous concept of chirality.https://www.mdpi.com/2073-8994/11/10/1320chirality definitionsymmetrymikowski spacetimeisometries
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Michel Petitjean
spellingShingle	Michel Petitjean About Chirality in Minkowski Spacetime Symmetry chirality definition symmetry mikowski spacetime isometries
author_facet	Michel Petitjean
author_sort	Michel Petitjean
title	About Chirality in Minkowski Spacetime
title_short	About Chirality in Minkowski Spacetime
title_full	About Chirality in Minkowski Spacetime
title_fullStr	About Chirality in Minkowski Spacetime
title_full_unstemmed	About Chirality in Minkowski Spacetime
title_sort	about chirality in minkowski spacetime
publisher	MDPI AG
series	Symmetry
issn	2073-8994
publishDate	2019-10-01
description	In this paper, we show that Lorentz boosts are direct isometries according to the recent mathematical definitions of direct and indirect isometries and of chirality, working for any metric space. Here, these definitions are extended to the Minkowski spacetime. We also show that the composition of parity inversion and time reversal is an indirect isometry, which is the opposite of what could be expected in Euclidean spaces. It is expected that the extended mathematical definition of chirality presented here can contribute to the unification of several definitions of chirality in space and in spacetime, and that it helps clarify the ubiquitous concept of chirality.
topic	chirality definition symmetry mikowski spacetime isometries
url	https://www.mdpi.com/2073-8994/11/10/1320
work_keys_str_mv	AT michelpetitjean aboutchiralityinminkowskispacetime
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About Chirality in Minkowski Spacetime

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