<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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| Format: | Article |
| Language: | English |
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MDPI AG
2020-05-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/12/5/817 |
| _version_ | 1797567917668171776 |
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| author | Martin Walker |
| author_facet | Martin Walker |
| author_sort | Martin Walker |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-03-10T19:48:57Z |
| format | Article |
| id | doaj.art-c85c7530c2be401790af0c23eec2f45f |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T19:48:57Z |
| publishDate | 2020-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-c85c7530c2be401790af0c23eec2f45f2023-11-20T00:34:33ZengMDPI AGSymmetry2073-89942020-05-0112581710.3390/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 |
| 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 |
| title | <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_short | <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 |
| 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 |