1654-9163 (print) ISSN 2001-7235 (online)
The Abraham Zelmanov Journal
The journal for General Relativity, gravitation and cosmology
Lichnérowicz’s Theory of Spinors in General Relativity: The Zelmanov Approach
In this paper, we apply Abraham Zelmanov’s theory of chronometric invariants to the spinor formalism, based on Lichnérowicz’s initial spinor formalism extended to the General Theory of Relativity. From the classical theory, we make use of the Dirac current which is shown to be a real four-vector, and by an appropriate choice of the compatible gamma matrices, this current retains all the properties of a space-time vector. Its components are uniquely expressed in terms of spinor components, and we eventually obtain the desired physically observable spinors in the sense of Zelmanov, next to the scalar, vector, and tensor quantities.
Ref: The Abraham Zelmanov Journal, 2012, volume 5, pages 117-133
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