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Reply to da Rocha and Rodrigues' comments on the orientation congruent algebra and twisted forms in electrodynamics
Author(s) -
Demers D.G.
Publication year - 2010
Publication title -
annalen der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.009
H-Index - 68
eISSN - 1521-3889
pISSN - 0003-3804
DOI - 10.1002/andp.201000045
Subject(s) - clifford algebra , rotation formalisms in three dimensions , clifford bundle , algebra over a field , multivector , invariant (physics) , mathematics , pure mathematics , associative property , geometric algebra , algebra representation , theoretical physics , physics , cellular algebra , vector bundle , mathematical physics , geometry , normal bundle , frame bundle
The recent claim by da Rocha and Rodrigues that the nonassociative orientation congruent algebra ( algebra) and native Clifford algebra are incompatible with the Clifford bundle approach is false. The new native Clifford bundle approach, in fact, subsumes the ordinary Clifford bundle one. Associativity is an unnecessarily too strong a requirement for physical applications. Consequently, we obtain a new principle of nonassociative irrelevance for physically meaningful formulas. In addition, the adoption of formalisms that respect the native representation of twisted (or odd) objects and physical quantities is required for the advancement of mathematics, physics, and engineering because they allow equations to be written in sign‐invariant form. This perspective simplifies the analysis of, resolves questions about, and ends needless controversies over the signs, orientations, and parities of physical quantities.