A conformally invariant theory of gravitation and electromagnetism

A formalism for the mathematical description of conformal gravity and its dynamical evolution based on the local twistor geometry is presented. It is shown that the electromagnetic field can be naturally incorporated into this scheme by a modification of the local twistor parallel transport law. The dynamical equations (the Bach equations for gravity and the Maxwell equations for the electromagnetic field) are obtained by varying a single quantity-the modified twistor connection.