Carmeli's method of gauge-free quantization of the electromagnetic field is extended to the case of the linearized equations of general relativity. The first-order Newman-Penrose equations with a particular choice of frames of reference and tetrad system are formulated in terms of functions over the group ${\mathrm{SU}}_2$ and all the field variables are expressed in terms of one complex function. The equation for this function is derived and a canonical gauge-free quantization procedure is carried out. Implications of these results to the problem of quantization of the exact (nonlinear) equations of general relativity are discussed.

• Received 28 May 1974

DOI:https://doi.org/10.1103/PhysRevD.10.2338