Internal quark symmetries and colour SU(3) entangled with Z3-graded Lorentz algebra
In the current version of QCD the quarks are described by ordinary Dirac fields, organized in the following internal symmetry multiplets: the SU(3) colour, the SU(2) flavour, and broken SU(3) providing the family triplets. In this paper we argue that internal and external (i.e. space-time) symmetrie...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2021-11-01
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| Series: | Nuclear Physics B |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0550321321002261 |
| _version_ | 1818741860447813632 |
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| author | Richard Kerner Jerzy Lukierski |
| author_facet | Richard Kerner Jerzy Lukierski |
| author_sort | Richard Kerner |
| collection | DOAJ |
| description | In the current version of QCD the quarks are described by ordinary Dirac fields, organized in the following internal symmetry multiplets: the SU(3) colour, the SU(2) flavour, and broken SU(3) providing the family triplets. In this paper we argue that internal and external (i.e. space-time) symmetries are entangled at least in the colour sector in order to introduce the spinorial quark fields in a way providing all the internal quark's degrees of freedom which do appear in the Standard Model. Because the SU(3) colour algebra is endowed with natural Z3-graded discrete automorphisms, in order to introduce entanglement the Z3-graded version of Lorentz algebra with its vectorial and spinorial realizations are considered. The colour multiplets of quarks are described by 12-component colour Dirac equations, with a Z3-graded triplet of masses (one real and a Lee-Wick complex conjugate pair). We show that all quarks in the Standard Model can be described by the 72-component master quark sextet of 12-component coloured Dirac fields, which is required in order to implement the faithful spinorial representation of the Z3-graded Lorentz transformations. |
| first_indexed | 2024-12-18T02:03:20Z |
| format | Article |
| id | doaj.art-12cc7c41e75f47238add1a079a1dbd3f |
| institution | Directory Open Access Journal |
| issn | 0550-3213 |
| language | English |
| last_indexed | 2024-12-18T02:03:20Z |
| publishDate | 2021-11-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Nuclear Physics B |
| spelling | doaj.art-12cc7c41e75f47238add1a079a1dbd3f2022-12-21T21:24:40ZengElsevierNuclear Physics B0550-32132021-11-01972115529Internal quark symmetries and colour SU(3) entangled with Z3-graded Lorentz algebraRichard Kerner0Jerzy Lukierski1Laboratoire de Physique Théorique de la Matière Condensée - CNRS URA 7600 - Sorbonne-Université, B.C. 121, 4 Place Jussieu 75005 Paris, France; Corresponding author.Institute of Theoretical Physics, Wrocław University, Plac Maxa Borna 9, Wrocław, PolandIn the current version of QCD the quarks are described by ordinary Dirac fields, organized in the following internal symmetry multiplets: the SU(3) colour, the SU(2) flavour, and broken SU(3) providing the family triplets. In this paper we argue that internal and external (i.e. space-time) symmetries are entangled at least in the colour sector in order to introduce the spinorial quark fields in a way providing all the internal quark's degrees of freedom which do appear in the Standard Model. Because the SU(3) colour algebra is endowed with natural Z3-graded discrete automorphisms, in order to introduce entanglement the Z3-graded version of Lorentz algebra with its vectorial and spinorial realizations are considered. The colour multiplets of quarks are described by 12-component colour Dirac equations, with a Z3-graded triplet of masses (one real and a Lee-Wick complex conjugate pair). We show that all quarks in the Standard Model can be described by the 72-component master quark sextet of 12-component coloured Dirac fields, which is required in order to implement the faithful spinorial representation of the Z3-graded Lorentz transformations.http://www.sciencedirect.com/science/article/pii/S0550321321002261 |
| spellingShingle | Richard Kerner Jerzy Lukierski Internal quark symmetries and colour SU(3) entangled with Z3-graded Lorentz algebra Nuclear Physics B |
| title | Internal quark symmetries and colour SU(3) entangled with Z3-graded Lorentz algebra |
| title_full | Internal quark symmetries and colour SU(3) entangled with Z3-graded Lorentz algebra |
| title_fullStr | Internal quark symmetries and colour SU(3) entangled with Z3-graded Lorentz algebra |
| title_full_unstemmed | Internal quark symmetries and colour SU(3) entangled with Z3-graded Lorentz algebra |
| title_short | Internal quark symmetries and colour SU(3) entangled with Z3-graded Lorentz algebra |
| title_sort | internal quark symmetries and colour su 3 entangled with z3 graded lorentz algebra |
| url | http://www.sciencedirect.com/science/article/pii/S0550321321002261 |
| work_keys_str_mv | AT richardkerner internalquarksymmetriesandcoloursu3entangledwithz3gradedlorentzalgebra AT jerzylukierski internalquarksymmetriesandcoloursu3entangledwithz3gradedlorentzalgebra |