<i>SU</i>(2) × <i>SU</i>(2) Algebras and the Lorentz Group <i>O</i>(3,3)

<i>SU</i>(2) × <i>SU</i>(2) Algebras and the Lorentz Group <i>O</i>(3,3)

The Lie algebra of the Lorentz group <i>O</i>(3,3) admits two types of <i>SU</i>(2) × <i>SU</i>(2) subalgebras: a standard form based on spatial rotation generators and a second form based on temporal rotation generators. The units of measurement for the conserved...

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Main Author: Martin Walker
Format: Article
Language:English
Published: MDPI AG 2020-05-01
Series:Symmetry
Subjects:
Lie algebra
<i>O</i>(3,3)
time rotation
Dirac
Noether
Online Access:https://www.mdpi.com/2073-8994/12/5/817
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spelling doaj-c85c7530c2be401790af0c23eec2f45f2020-11-25T03:14:01ZengMDPI AGSymmetry2073-89942020-05-011281781710.3390/sym12050817<i>SU</i>(2) × <i>SU</i>(2) Algebras and the Lorentz Group <i>O</i>(3,3)Martin Walker0Independent Researcher, 3958 Grandis Place, Victoria, BC V8N 4H6, Canada The Lie algebra of the Lorentz group <i>O</i>(3,3) admits two types of <i>SU</i>(2) × <i>SU</i>(2) subalgebras: a standard form based on spatial rotation generators and a second form based on temporal rotation generators. The units of measurement for the conserved quantity due to invariance under temporal rotations are investigated and found to be the same units of measure as the Planck constant. The breaking of time reversal symmetry is considered and found to affect the chiral properties of a temporal <i>SU</i>(2) × <i>SU</i>(2) algebra. Finally, the symmetry between algebras is explored and pairs of algebras are found to be related by <i>SU</i>(2) × <i>U</i>(1) symmetry, while a group of three algebras are related by <i>SO</i>(4) symmetry.https://www.mdpi.com/2073-8994/12/5/817Lie algebra<i>O</i>(3,3)time rotationDiracNoether
collection DOAJ
language English
format Article
sources DOAJ
author Martin Walker
spellingShingle Martin Walker
<i>SU</i>(2) × <i>SU</i>(2) Algebras and the Lorentz Group <i>O</i>(3,3)
Symmetry
Lie algebra
<i>O</i>(3,3)
time rotation
Dirac
Noether
author_facet Martin Walker
author_sort Martin Walker
title <i>SU</i>(2) × <i>SU</i>(2) Algebras and the Lorentz Group <i>O</i>(3,3)
title_short <i>SU</i>(2) × <i>SU</i>(2) Algebras and the Lorentz Group <i>O</i>(3,3)
title_full <i>SU</i>(2) × <i>SU</i>(2) Algebras and the Lorentz Group <i>O</i>(3,3)
title_fullStr <i>SU</i>(2) × <i>SU</i>(2) Algebras and the Lorentz Group <i>O</i>(3,3)
title_full_unstemmed <i>SU</i>(2) × <i>SU</i>(2) Algebras and the Lorentz Group <i>O</i>(3,3)
title_sort <i>su</i>(2) × <i>su</i>(2) algebras and the lorentz group <i>o</i>(3,3)
publisher MDPI AG
series Symmetry
issn 2073-8994
publishDate 2020-05-01
description The Lie algebra of the Lorentz group <i>O</i>(3,3) admits two types of <i>SU</i>(2) × <i>SU</i>(2) subalgebras: a standard form based on spatial rotation generators and a second form based on temporal rotation generators. The units of measurement for the conserved quantity due to invariance under temporal rotations are investigated and found to be the same units of measure as the Planck constant. The breaking of time reversal symmetry is considered and found to affect the chiral properties of a temporal <i>SU</i>(2) × <i>SU</i>(2) algebra. Finally, the symmetry between algebras is explored and pairs of algebras are found to be related by <i>SU</i>(2) × <i>U</i>(1) symmetry, while a group of three algebras are related by <i>SO</i>(4) symmetry.
topic Lie algebra
<i>O</i>(3,3)
time rotation
Dirac
Noether
url https://www.mdpi.com/2073-8994/12/5/817
work_keys_str_mv AT martinwalker isui2isui2algebrasandthelorentzgroupioi33
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