The Metric Dirac Equation Revisited and the Geometry of Spinors by Norbert Schwarzer
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Overview: Subjecting this scaled metric in the usual way to the Einstein-Hilbert action [A2] does not only present us with Quantum Einstein-Field-Equations [A3] and thus, a quantized version of Einstein’s General Theory of Relativity [A4], but – along the way (e.g. [A5 – A10]) – gives us the classical quantum equations. Also, thermodynamics can be derived from, respectively found inside this simple scaled metric approach [A3, A10].
With the Klein-Gordon equation, already falling out of our new approach – which could just be seen as another form of variation, by the way – we may just set back and conclude that this way we also have obtained the Dirac equation [A11]. This namely was classically derived by an operator factorization from the Klein-Gordon equation. Thus, having obtained the latter, automatically gives us the Dirac equation, too. However, when digging deeper (metrically) and also trying to find a completely metric origin and understanding of the Dirac approach, we have to come to the conclusion that the simple scalar metric scaling with F[f] does not suffice. We find that only a vector scaling will probably give us the complete picture [A12].
** For convenience we will repeat these derivations for the Klein-Gordon and the Schrцdinger equation in the appendices of this paper.
Genre: Non-Fiction > Educational
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