# Rendering SU(3) intuitive: Symmetries of Lorentz tensors

Abstract : Under a Lorentz transformation of the electromagnetic field (E, cB) the quantity E$^2$ − c$^2$B$^2$ remains preserved. A Lorentz transformation does not preserve the energy density ε$_0$ (E$^2$ + c$^2$B$^2$) of the field. One can thus ask which are the transformations that preserve the quantity E$^2$ + c$^2$B$^2$. We show that the symmetry group of such transformations is isomorphic to SU(3). We can thus use these transformations of the electromagnetic field as a model to visualize what happens in SU(3) by analogy, just like we can use the rotation group SU(2) as a model to visualize what happens in the isospin group SU(2) by analogy.
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Preprints, Working Papers, ...

https://hal-cea.archives-ouvertes.fr/cea-01720356
Contributor : Gerrit Coddens Connect in order to contact the contributor
Submitted on : Thursday, March 1, 2018 - 10:30:44 AM
Last modification on : Tuesday, July 6, 2021 - 3:19:25 AM
Long-term archiving on: : Wednesday, May 30, 2018 - 12:50:27 PM

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• HAL Id : cea-01720356, version 1

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### Citation

Gerrit Coddens. Rendering SU(3) intuitive: Symmetries of Lorentz tensors. 2018. ⟨cea-01720356⟩

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