Variational Principles for Constrained Electromagnetic Field and Papapetrou Equation

Abstract

In our previous article [4] an approach to derive Papapetrou equations for constrained electromagnetic field was demonstrated by use of field variational principles. The aim of current work is to present more universal technique of deduction of the equations which could be applied to another types of non-scalar fields. It is based on Noether theorem formulated in terms of Cartan' formalism of orthonormal frames. Under infinitesimal coordinate transformation the one leads to equation which includes volume force of spin-gravitational interaction. Papapetrou equation for vector of propagation of the wave is derived on base of the equation. Such manner of deduction allows to formulate more accurately the constraints and clarify equations for the potential and for spin.