A graphical consistency check between the fundamental and alternative flux operators in loop quantum gravity fixes the volume-operator constant κ_reg to 1/2.
Loop Quantum Brans-Dicke Theory
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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.
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Consistency check on the fundamental and alternative flux operators in loop quantum gravity
A graphical consistency check between the fundamental and alternative flux operators in loop quantum gravity fixes the volume-operator constant κ_reg to 1/2.