Loop quantum brans-dicke theory

The loop quantization of Brans-Dicke theory (with coupling parameter ω = 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 conguration 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 denined operator to represent quantum dynamics. This formalism enable us to extend the scheme of non-perturbative loop quantum gravity to the Brans-Dicke theory.