A coordinate-free form of the Dirac equation for the electron. (English. Russian original) Zbl 1138.81392

Dokl. Math. 68, No. 2, 281-284 (2003); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 392, No. 3, 317-321 (2003).
Summary: The Dirac equation for the electron is represented in a new invariant (coordinate-free) form with the use of exterior forms and differential operators \(d\) and \(\delta\). The suggested form is invariant under changes of coordinates from the Lorentz group of proper orthochronous transformations. The suggested approach differs from that of N.G.Marchuk [Nuovo Cimento 117B, No. 5, 511 (2002)] in that the wave function of the suggested equation belongs to a minimal left ideal of the algebra of exterior forms with respect to Clifford multiplication.


81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
58A15 Exterior differential systems (Cartan theory)