Metric gravity as a non-quantized Higgs field

If gravity is a pseudo-Riemannian metric, it is a Higgs field. Being a Higgs field, a metric gravitational field is non-quantized.

Classical field theory is adequately described in terms of fibre bundles (Archiv). Classical gravitation theory formulated in these terms is metric-affine theory whose dynamic variables are a pseudo-Riemannian metric, treated as a metric gravitational field, and a general linear connection on a world manifold X.

We concentrate our attention to a metric gravitation field.  A pseudo-Riemannian metric on a world manifold X is defined as a global section of the quotient LX/SO(1,3) of the linear frame bundle LX by the Lorentz group SO(1,3). Therefore, it exemplifies a Higgs field in classical field theory on fibre bundles.

Its Higgs character is displayed as follows. Given different pseudo-Riemannian metrics g and g', the representations of the holonomic coframes dx by the Dirac matrices acting on Dirac spinor fields are not equivalent.

It follows that a Dirac spinor field can not be considered in the case of a superposition of different metric gravitational fields. Therefore, quantization of a metric gravitational field fails to satisfy the superposition principle, and we think that it is non-quantized.

References:

G. Sardanashvily, Metric gravity as a non-quantized Higgs field (2010).