Abstract
The present paper is a mathematical comment on a paper by Treder (Treder, 1970). The metric tensorg reduces the tangent bundleT of a space-time to the tangent Lorentz bundleL. The Levi-Civita connection inT induces in a natural way connections inL, and in the tensor product bundles ofT, L, and the spinor bundleS. These connections are ‘the general Lorentz-covariant connection’ by Treder. It is possible to treat the local tetrad field components as local components of a global cross-section of L⊗T, with vanishing general Lorentz-covariant derivative.
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References
Bräuer, H.-J. (1970). Spinorbündel in der Physik. Dissertation DAW Berlin.
Geroch, R. (1968). Spinor Structure of Space-Times in General Relativity I.Journal of Mathematical Physics, Vol. 9, No. 11.
Steenrod, N. (1951).The Topology of Fibre Bundles. Princeton, N.J.
Treder, H.-J. (1970). General Relativity and General Lorentz-covariance.International Journal of Theoretical Physics, Vol. 3, No. 1, pp. 23–31.
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I wish to thank Professor H.-J. Treder for his interest and for valuable discussions.
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Bräuer, HJ. Remark on general Lorentz-covariance. Int J Theor Phys 4, 243–246 (1971). https://doi.org/10.1007/BF00674277
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DOI: https://doi.org/10.1007/BF00674277