Geometric Structure of the Translation Gauge Theory of Gravitation
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概要
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In the translation gauge theory of gravitation, we give a general expression of the affine connexion coefficient satisfying the following conditions : (i) It is a function of the vierbein b_k^μ and of its first derivative b_k^μ,v. (ii) It is linear in b_k^μ,v. (iii) It satisfies the metricity condition. Our expression includes both of the connexion coefficients of the Riemann and Weitzenbock space-times as special ones, and hence, the space-time in the translation gauge theory is of Riemann-Cartan type. We fix the gravitational interaction of matter fields following Hayashi's method. The most general quadratic Lagrangian density of b_k^μ is represented in terms of the curvature scalar and of the torsion tensor. In the case of electromagnetic field interacting with gravitational field, it is pointed out that the torsion tensor can give rise to observable effects if the field strength J_<μν> of the electromagnetic field is given by J_<μν>=∇ _μA_ν-∇ _νA_μ. Besides the electric charge of the matter field there is a charge which is associated both with the gravitational and electromagnetic fields. In the case of the electromagnetic and gravitational fields produced by a spherically symmetric massive charge matter, the effects of the torsion tensor appear in the post-Newtonian term in the gravitational potential and in the "post-Coulombian term" in the electric field strength. We point out the available experimental data in the astronomy impose no restriction on the connexion coefficient.
- 理論物理学刊行会の論文
- 1982-04-25
著者
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Yoshida Hideo
Department Of Aeronautics And Astronautics Kyoto University
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YOSHIDA Hideo
Department of Physics, Osaka City University
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