Abstract
The linear approximation of the theory of the spinor gauge field (TSGF), introduced in the localization of the group of tetrad Lorentz transformations, is discussed. In constructing the TSGF, use is made of the principle of correspondence with the tetrad theory of gravitation in a space of absolute parallelism. It is shown that the imposing of additional conditions of the Lorentz-Hilbert type in the linearized TSGF leads to a unique definition of the Lagrangian of the A-field, quadratic in the field intensity, of the form RαβγσRαβγσ. which is usually postulated from considerations of simplicity and by analogy with other gauge fields. Two new identities in a space with torsion are proved.
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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 74–79, September, 1979.
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Tunyak, V.N. Quadratic lagrangians in a space with torsion and the theory of the spinor gauge field. Soviet Physics Journal 22, 985–989 (1979). https://doi.org/10.1007/BF00891397
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DOI: https://doi.org/10.1007/BF00891397