Towards the deformation quantization of linearized gravity

Nuclear Physics B, 1996

We describe a deformation of the observable algebra of quantum gravity in which the loop algebra is extended to framed loops. This allows an alternative nonperturbative quantization which is suitable for describing a phase of quantum gravity characterized by states which are normalizable in the measure of Chern-Simons theory. The deformation parameter, q, is e ih 2 G 2 Λ/6 , where Λ is the cosmological constant. The Mandelstam identities are extended to a set of relations which are governed by the Kauffman bracket so that the spin network basis is deformed to a basis of SU (2) q spin networks. Corrections to the actions of operators in non-perturbative quantum gravity may be readily computed using recoupling theory; the example of the area observable is treated here. Finally, eigenstates of the q-deformed Wilson loops are constructed, which may make possible the construction of a q-deformed connection representation through an inverse transform.

2016

Developing Planck scale physics requires addressing problem of time, quantum reduction, determinism and continuum limit. In this article on the already known foundations of quantum mechanics, a set of proposals of dynamics is built on fully constrained discrete models: 1) Self-Evolution - Flow of time in the phase space in a single point system, 2) Local Measurement by Local Reduction through quantum diffusion theory, quantum diffusion equation is rederived with different assumptions, 3) Quantum Evolution of a MultiPoint Discrete Manifold of systems through a foliation chosen dynamically, and 4) Continuum Limit, and Determinism are enforced by adding terms and averaging to the action. The proposals are applied to the various physical scenarios such as: 1) Minisuperspace reduced cosmology of isotropic and homogenous universe with scalar field, 2) Expanding universe with perturbation, and 3) Newtonian universe. Ways to experimentally test the theory is discussed. This article is a fur...

Int.J.Mod.Phys. A30 (2015) 1550016

Emergent gravity is based on a novel form of the equivalence principle known as the Darboux theorem or the Moser lemma in symplectic geometry stating that the electromagnetic force can always be eliminated by a local coordinate transformation as far as spacetime admits a symplectic structure, in other words, a microscopic spacetime becomes noncommutative (NC). If gravity emerges from U(1) gauge theory on NC spacetime, this picture of emergent gravity suggests a completely new quantization scheme where quantum gravity is defined by quantizing spacetime itself, leading to a dynamical NC spacetime. Therefore the quantization of emergent gravity is radically different from the conventional approach trying to quantize a phase space of metric fields. This approach for quantum gravity allows a background independent formulation where spacetime as well as matter fields is equally emergent from a universal vacuum of quantum gravity.

2010

."but we do not have quantum gravity." This fraze is often used when analysis of a physical problem enters the regime in which quantum gravity effects should be taken into account. In fact, there are several models of the gravitational field coupled to (scalar) fields for which the quantization procedure can be completed using loop quantum gravity techniques. The model we present in this paper consist of the gravitational field coupled to a scalar field. The result has similar structure to the loop quantum cosmology models, except for that it involves all the local degrees of freedom because no symmetry reduction has been performed at the classical level.

Annals of Physics, 1978

Physics Letters A, 2008

Nonholonomic distributions and adapted frame structures on (pseudo) Riemannian manifolds of even dimension are employed to build structures equivalent to almost Kähler geometry and which allows to perform a Fedosov-like quantization of gravity. The nonlinear connection formalism that was formally elaborated for Lagrange and Finsler geometry is implemented in classical and quantum Einstein gravity.

Advances in High Energy Physics, 2018

A Hamiltonian formulation of General Relativity within the context of the Nexus Paradigm of quantum gravity is presented. We show that the Ricci flow in a compact matter free manifold serves as the Hamiltonian density of the vacuum as well as a time evolution operator for the vacuum energy density. The metric tensor of GR is expressed in terms of the Bloch energy eigenstate functions of the quantum vacuum allowing an interpretation of GR in terms of the fundamental concepts of quantum mechanics.

The European physical journal. C, Particles and fields

Based on certain assumptions for the expectation value of a product of the quantum fluctuating metric at two points, the gravitational and scalar field Lagrangians are evaluated. Assuming a vanishing expectation value of the first-order terms of the metric, the calculations are performed with an accuracy of second order. It is shown that such quantum corrections give rise to modified gravity.

J Geom Physics, 2010

A geometric procedure is elaborated for transforming (pseudo) Riemanian metrics and connections into canonical geometric objects (metric and nonlinear and linear connections) for effective Lagrange, or Finsler, geometries which, in turn, can be equivalently represented as almost Kähler spaces. This allows us to formulate an approach to quantum gravity following standard methods of deformation quantization. Such constructions are performed not on tangent bundles, as in usual Finsler geometry, but on spacetimes enabled with nonholonomic distributions defining 2+2 splitting with associate nonlinear connection structure. We also show how the Einstein equations can be written in terms of Lagrange-Finsler variables and corresponding almost symplectic structures and encoded into the zero-degree cohomology coefficient for a quantum model of Einstein manifolds.

1994

A suggestion is made for quantizing gravity perturbatively, and is illustrated for the example of a massive scalar field with gravity.