The Clifford algebra of differential forms
Clifford algebras are discussed in the realization of differential forms in Minkowski space-time. Explicit solutions of the Klein-Gordon equation and the Kähler-Dirac equation in this realization are constructed. An important result is that a massive spin-1/2 particle cannot be mathematically accommodated in real Minkowski space with metric \((-1,-1,- 1,+1)\); such a particle can be accommodated either in the Majorana representation of the Dirac algebra with metric \((+1,+1,+1,-1)\) or in a complex Clifford algebra.
scientific article; zbMATH DE number 3912547
scientific article