Loop Quantum Brans-Dicke Theory

The loop quantization of Brans-Dicke theory (with coupling parameter ω not equal -3/2 is studied. In the geometry-dynamical formalism, the canonical structure and constraint algebra of this theory are similar to those of general relativity coupled with a scalar field. The connection dynamical formalism of the Brans-Dicke theory with real su(2)-connections as configuration variables is obtained by canonical transformations. The quantum kinematical Hilbert space of Brans-Dicke theory is constituted as that of loop quantum gravity coupled with a polymer-like scalar field. The Hamiltonian constraint is promoted as a well defined operator to represent quantum dynamics. This formalism enable us to extend the scheme of non-perturbative loop quantum gravity to the Brans-Dicke theory.