Gravitational Gauge Theory Developed Based on the Stephenson-Kilmister-Yang Equation

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A Yang-Mills formulation of Einstein gravity with spin-affine connection as the dynamical variable of gravitational field is suggested based on the Stephenson-Kilmister-Yang (SKY) equation. A physically interesting property of the present formalism is that the Einstein field equation appears as a first-integral solution to the Yang-Mills type gravitational gauge field equation. The gravitational current density, the law of conservation and the gravitational gauge field strength in vierbein formulation are discussed. The present scheme could provide us with new insight into a possible way to include both Yang-Mills field and gravitational gauge field into one framework of generalized vierbein fields.

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