Loop Quantum Brans-Dicke Theory

TL;DR

This paper extends loop quantum gravity techniques to Brans-Dicke theory, establishing a canonical framework, quantization scheme, and Hamiltonian operator, thus enabling non-perturbative quantum analysis of this scalar-tensor gravity model.

Contribution

It develops a loop quantum gravity formalism for Brans-Dicke theory, including the canonical structure, connection variables, and a well-defined Hamiltonian operator.

Findings

Canonical structure similar to general relativity with scalar field

Quantum kinematical Hilbert space constructed with polymer scalar field

Hamiltonian constraint promoted to a well-defined quantum operator

Abstract

The loop quantization of Brans-Dicke theory (with coupling parameter $\omega\neq-3/2$) 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 of that 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.