50-component Theory for Spin 2 Particle, Plane Wave Solutions, Massive and Massless Cases

Abstract

It is known a 50-component theory for a spin 2 particle with the anomalous magnetic moment, invariant under the Lorentz group and based on the use of symmetric 2-nd rank tensor and a 3-rd rank tensor symmetric in two indices. Their symmetries are similar to these of the metric tensor and Christoffel symbols of General relativity. By eliminating the 3-rd rank tensor we derive a system of 2-nd order 10 equations for symmetric tensor. This system is studied for plane wave solutions. In massive case, we have found 5 independent solutions. Separately, we have examined the case of a massless field. There are found 6 independent solutions, 4 special combinations of them are identified with the gauge solutions in accordance with Pauli - Fierz approach. Finally we have found two solutions which do not contain any gauge components.