Graviton as a Symmetry-Breaking Solution on Lorentz Invariance. I

An attempt to realize graviton as a Nambu-Goldstone particle has been made on the basis of the spontaneous breakdown of Lorentz in variance. By applying this· spontaneous breakdown, an interacting system of a neutral vector field and a symmetric tensor field is · considered. The symmetric tensor field is composed of the trace part and the traceless diver­ genceless part. The tensor current of the neutral vector field is given in a general form. The breakdown of Lorentz invariance is achieved by. making only the time-time component of the vacuum expectation value of the tensor current nonvanished. From Dyson's equation for the interacting system, it is proved that the ,renormalized tensor field propagator has a massless pole, when the Hartree condition is satisfied for this breakdown. To get better understanding on this spontaneous breakdown, the. formal theory by Bludman and Klein is also adopted, where the same conclusion is derived.