Gilton, Marian (2024) Noether's Ledger: Interpreting Charge Conservation in non-Abelian Gauge Theories. [Preprint]
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Abstract
The application of Noether's theorem to the exact SU(3) color symmetry of quantum chromodynamics results in the conservation of the color charge current. This current takes values in SU(3)'s Lie algebra, and it is therefore eight-dimensional. But how can this eight-dimensional space be the right mathematical object for the conservation of the three color charges 'red', 'blue', and 'green' and their three corresponding anti-colors? We might have expected a six-dimensional space, or perhaps a nine-dimensional one, but eight is surprising. This paper answers this question through explicit construction of the SU(3) adjoint representation from the two fundamental representations of SU(3). This construction generates principled reasons for interpreting elements of the SU(3) Lie algebra as bearing combinations of color and anti-color. In light of this construction, this paper contrasts mathematical and conceptual features of color charge conservation with electric charge conservation, thereby highlighting some of the challenges and subtleties of interpreting non-Abelian gauge theories.
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| Item Type: | Preprint | ||||||
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| Keywords: | Noether's theorem, color charge, charge conservation, non-Abelian gauge theory, Lie algebra valued quantities. | ||||||
| Subjects: | Specific Sciences > Physics > Fields and Particles Specific Sciences > Physics Specific Sciences > Physics > Quantum Field Theory Specific Sciences > Physics > Symmetries/Invariances |
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| Depositing User: | Marian J. R. Gilton | ||||||
| Date Deposited: | 04 Dec 2024 13:19 | ||||||
| Last Modified: | 04 Dec 2024 13:19 | ||||||
| Item ID: | 24185 | ||||||
| Subjects: | Specific Sciences > Physics > Fields and Particles Specific Sciences > Physics Specific Sciences > Physics > Quantum Field Theory Specific Sciences > Physics > Symmetries/Invariances |
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| Date: | 11 October 2024 | ||||||
| URI: | https://philsci-archive.pitt.edu/id/eprint/24185 |
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