Hamiltonian formulation of gravity as a spontaneously-broken gauge theory of the Lorentz group

A number of approaches to gravitation have much in common with the gauge theories of the standard model of particle physics. In this paper, we develop the Hamiltonian formulation of a class of gravitational theories that may be regarded as spontaneously-broken gauge theories of the complexified Lorentz group SO(1,3)C with the gravitational field described entirely by a gauge field valued in the Lie algebra of SO(1,3)C and a 'Higgs field' valued in the group's fundamental representation. The theories have one free parameter beta which appears in a similar role to the inverse of the Barbero-Immirzi parameter of Einstein-Cartan theory. However, contrary to that parameter, it is shown that the number of degrees of freedom (DOFs) crucially depends on the value of beta. For non-zero values of beta, it is shown the theories possesses three complex DOFs, and for the specific values beta=+/- i an extension to general relativity is recovered in a symmetry-broken regime. For the value beta = 0, the theory possesses no local DOFs. A non-zero value of beta corresponds to the self-dual and anti-self-dual gauge fields appearing asymmetrically in the action, therefore in these models, the existence of gravitational DOFs is tied to chiral asymmetry in the gravitational sector.