Nichtlineare Spinorgleichungen und affiner Zusammenhang
Open Access
- 1 August 1964
- journal article
- Published by Walter de Gruyter GmbH in Zeitschrift für Naturforschung A
- Vol. 19 (7-8) , 825-827
- https://doi.org/10.1515/zna-1964-7-801
Abstract
It is shown that the non-linear term of the HEisENBERG-PAULi-equation can be interpreted as torsion of space-time in the following way. The wavefuinction is subjected to a (non-rigid) LORENTZ-transformation varying from point to point: ψ = Sψ'. If the matrix S=S(x) is chosen so that it satisfies the equation γλ(∂S/∂xλ) S-1+l2γλγ5 ψ̅ γλγ5ψ=0, than the non-linear term of the H.-P.-equation vanishes in the system x'; i. e. with (∂xλ/∂xμ′) γμ=S-1 γλ S one has 0=γλ(∂ψ/∂xλ) +l2γλγ5 ψ ψ̅ γλ γ5 ψ ≡ S γμ (∂ψ'/∂xμ′). This result holds also in the case where the H.-P.-equation contains still a term with γλ ψ̅ γλ ψ and/or γλ Αλ (Aλ = electro-magnetic potential), provided Aλ satisfies the LoRENTz-condition ∂Aλ/∂xλ=0. The proof is a follows: Taking a representation of S in the DIRAC-ring, the equation which determines S splits into 8 equations. Between these equations there exist 2 identities (which correspond to the PAULI—GuRSEY-transformation resp. LoRENTz-condition); so one finally has 6 equations for the determination of the 6 parameters of S.Keywords
This publication has 0 references indexed in Scilit: