A relativistic theory of the field II: Hamilton's principle and Bianchi's identities

As gravitation and electromagnetism are closely analogous long-range interactions, and the current formulation of gravitation is given in terms of geometry. Thence emerges a relativistic theory of the field by generalization of the general relativity. The derivation presented shows how naturally we can extend general relativity theory to a non-symmetric field, and that the field-equations are really the generalizations of the gravitational equations. With curvature tensor and the variational principle, we will deduce the field equations and Bianchi's identities. In consecuense, the field equations will find from Bianchi's identities.