Loop Quantum Brans-Dicke Theory

Abstract

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

4 pages, to appear in Journal of Physics: Conference Series (JPCS)

References in corpus (6)

• Dark Energy and the Accelerating Universe
• Hamiltonian Formulation of Palatini f(R) theories a la Brans-Dicke
• Extension of loop quantum gravity to $f(R)$ theories
• New length operator for loop quantum gravity
• Loop quantum $f(R)$ theories
• Nonperturbative Loop Quantization of Scalar-Tensor Theories of Gravity

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• Background dynamics of pre-inflationary scenario in Brans-Dicke loop quantum cosmology
• Loop quantum gravity and cosmological constant
• Consistency check on the fundamental and alternative flux operators in loop quantum gravity
• Loop quantum modified gravity and its cosmological application
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• Conformally Invariant Brans-Dicke Loop Quantum Cosmology: A Quantum Geometric Model of Linking Theory
• Deparametrization and quantization of scalar-tensor gravity and its cosmological model
• Loop quantum cosmological model from ADM Hamiltonian
• Degenerate Limits of Scalar-Tensor Gravity
• Hamiltonian Theory: generalizations to higher dimensions, supersymmetry and modified gravity
• Mechanics of Isolated Horizons in Scalar-Tensor Theories