Loop quantum gravity coupled to a scalar field

Abstract

We reconsider the Rovelli-Smolin model of gravity coupled to the Klein-Gordon time field with an eye towards capturing the degrees of freedom of the scalar field lost in the framework in which time is deparametrized by the scalar field. Several new results for loop quantum gravity are obtained: (i) a Hilbert space for the gravity-matter system and a non-standard representation of the scalar field thereon is constructed, (ii) a new operator for the scalar constraint of the coupled system is defined and investigated, (iii) methods for solving the constraint are developed. Commutators of the new constraint do not vanish, but seem to reproduce a part of the Dirac algebra. This, however, poses problems for finding solutions. Hence the states we consider -- and perhaps the whole setup -- still needs some improvement. As a side result we describe a representation of the gravitational degrees of freedom in which the flux is diagonal. This representation bears a strong resemblance to the BF vacuum of Dittrich and Geiller.

18 pages

References in corpus (6)

• Gravity quantized
• A symmetric scalar constraint for loop quantum gravity
• Flux formulation of loop quantum gravity: Classical framework
• Dynamical Quantum Geometry (DQG Programme)
• On loop quantum gravity kinematics with non-degenerate spatial background
• The Koslowski-Sahlmann representation: Quantum Configuration Space

Cited by in corpus (16)

• Group field theory for quantum gravity minimally coupled to a scalar field
• Loop Quantum Gravity on Dynamical Lattice and Improved Cosmological Effective Dynamics with Inflaton
• Generalized Ashtekar variables for Palatini f(R) models
• Closing the gaps in quantum space and time: Conformally augmented gauge structure of gravitation
• Towards a dual spin network basis for (3+1)d lattice gauge theories and topological phases
• Immirzi parameter without Immirzi ambiguity: Conformal loop quantization of scalar-tensor gravity
• Canonical loop quantization of the lowest-order projectable Horava gravity
• The continuum approach to the BF vacuum: the U(1) case
• A new realization of quantum geometry
• Exploring the Tomlin-Varadarajan quantum constraints in $U(1{)}^3$ loop quantum gravity: solutions and the Minkowski theorem
• A Fock space structure for the diffeomorphism invariant Hilbert space of loop quantum gravity and its applications
• Loop Quantum Vector-Tensor Gravity and Its Spherically Symmetric Model
• A note on conformally compactified connection dynamics tailored for anti-de Sitter space
• Deparametrization and quantization of scalar-tensor gravity and its cosmological model
• Realization of Dirac quantization in loop quantum gravity
• Connection Dynamics of Reduced 5-dimensional Kaluza-Klein Theory and Its Deparametrization