Gauging octonion algebra
A. K. Waldron, G. C. Joshi
Abstract
By consireding representation theory for non-associative algebras we construct the fundamental and adjoint representations of the octonion algebra. We then show how these representations by associative matrices allow a consistent octonionic gauge theory to be realised. We find that non-associativity implies the existence of new terms in the transformation laws of fields and the kinetic term of an octonionic Lagrangian.
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