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A Solvable Algebra for Massless Fermions
Version 1
: Received: 9 July 2022 / Approved: 11 July 2022 / Online: 11 July 2022 (12:15:43 CEST)
A peer-reviewed article of this Preprint also exists.
Groote, S.; Saar, R. A Solvable Algebra for Massless Fermions. Symmetry 2024, 16, 97, doi:10.3390/sym16010097. Groote, S.; Saar, R. A Solvable Algebra for Massless Fermions. Symmetry 2024, 16, 97, doi:10.3390/sym16010097.
Abstract
We derive the stabiliser group of the four-vector, also known as Wigner’s little group, in case of massless particle states, as the maximal solvable subgroup of the proper orthochronous Lorentz group of dimension four, known as the Borel subgroup. In the absence of mass, particle states are disentangled into left and right handed chiral states, governed by the maximal solvable subgroups sol2± of order two. Induced Lorentz transformations are constructed and applied to general representations of particle states. Finally, it is argued how the spin-flip contribution is closely related to the occurrence of nonphysical spin operators.
Keywords
Solvable Lie group; Borel subgroup; massless particle states; chirality states
Subject
Physical Sciences, Mathematical Physics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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