2011

Nonperturbative Loop Quantization of Scalar-Tensor Theories of Gravity

Zhang, Xiangdong, Ma, Yongge

Understand

The Hamiltonian formulation of scalar-tensor theories of gravity is derived from their Lagrangian formulation by Hamiltonian analysis.

The Hamiltonian formalism marks off two sectors of the theories by the coupling parameter $\omega(\phi)$.
In the sector of $\omega(\phi)=-3/2$, the feasible theories are restricted and a new primary constraint generating conformal transformations of spacetime is obtained, while in the other sector of $\omega(\phi)\neq-3/2$, the canonical structure and constraint algebra of the theories are similar to those of general relativity coupled with a scalar field.
By canonical transformations, we further obtain the connection dynamical formalism of the scalar-tensor theories with real $su(2)$-connections as configuration variables in both sectors.

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