Exceptional ${\mathfrak{g}}_2$ deformations and gauge symmetries

Abstract

Deformed ${\mathfrak{g}}_2$ exceptional applications are introduced via the Clifford algebra-parametrized formalism. Using the products between multivectors of $\cl_{0,7}$, the Clifford algebra over the metric vector space $\RR^{0,7}$, and octonions, resulting in an octonion, we generalize the exceptional Lie algebra ${\mathfrak{g}}_2$ applications, also associated with the transformation rules for bosonic and fermionic fields on the 7-sphere $S^7$. The emergence of $SU(3)$-like subalgebras within the exceptional Lie algebra ${\mathfrak{g}}_2$ provides an algebraic framework reminiscent of the $SU(3)$ gauge symmetry of QCD.

12 pages