https://wiki.naturalphilosophy.org/index.php?action=history&feed=atom&title=Carl_Brannen 2026-07-18T06:12:53Z Revision history for this page on the wiki MediaWiki 1.43.0 https://wiki.naturalphilosophy.org/index.php?title=Carl_Brannen&diff=292413&oldid=prev 2026-07-18T02:18:05Z

<p>Create biographical page for person listed in The Worldwide List of Dissident Scientists (web-verified; red-link batch 6)</p> <p><b>New page</b></p><div>{{Infobox scientist<br /> | name = Carl Brannen<br /> | fields = Theoretical physics<br /> | known_for = Circulant-matrix (density-matrix) derivation of the Koide lepton mass formula<br /> }}<br /> <br /> &#039;&#039;&#039;Carl Brannen&#039;&#039;&#039; is an independent physicist and author known for his work on elementary-particle mass formulas and a reformulation of quantum mechanics based on the density-matrix formalism. He is listed in &#039;&#039;[[The Worldwide List of Dissident Scientists]]&#039;&#039;.<br /> <br /> ==Work==<br /> Brannen works outside the academic mainstream on the foundations of particle physics, publishing his papers and notes through his personal website, brannenworks.com, and on preprint and repository sites. Rather than the usual state-vector (wavefunction) description of quantum mechanics, he develops a density-matrix (density-operator) formulation, which he expresses using Clifford algebra — a generalization of the Dirac gamma matrices. He has described this approach as analogous to the geometric-algebra program associated with David Hestenes, but applied to the density matrix instead of the state vector.<br /> <br /> He is best known for reformulating the Koide formula — an empirical relation among the charged-lepton (electron, muon, tau) masses proposed by Yoshio Koide — as an eigenvector/eigenvalue equation, writing the lepton masses as the squares of the eigenvalues of a circulant matrix, and extending the idea to propose corresponding predictions for the neutrino masses. This work has been cited in the physics literature discussing the Koide relation.<br /> <br /> ==External links==<br /> * [http://brannenworks.com/ brannenworks.com (personal site)]<br /> * [https://arxiv.org/pdf/1201.2067 &quot;The Koide Lepton Mass Formula and Geometry of Circles&quot; (arXiv)]<br /> * [https://independent.academia.edu/CarlBrannen Carl Brannen on Academia.edu]<br /> <br /> [[Category:Scientist|Brannen Carl]]<br /> [[Category:Worldwide List of Dissident Scientists]]</div>

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