Gravity induced by the Local SL(2,C) Transformation

概要

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It is insisted that the local SL (2,C) transformation of a spin basis ω_A generates not only the local SO_0(3,1) transformation of a Lorentz basis E_<μ__->, but also the extended GL (4,R) transformation of a coordinate basis ∂_μ. The two bases E_<μ__->, and ∂_μ are chosen, at the outset, so as to coincide with each other in the flat spacetime. The separation of two bases E_<μ__-> and ∂_μ suggests at once the existence of a field h_μ^υ which connects them. Using this field it is shown that the invariant action under the local SL (2,C) transformation leads to the Einstein's theory of gravity including the extension to the case that a matter field q is a spinor, provided that the original action is invariant under the Poincare transformation.
岡山理科大学の論文