The G_Newton --> 0 Limit of Euclidean Quantum Gravity

Abstract

Using the Ashtekar formulation, it is shown that the G_{Newton} --> 0 limit of Euclidean or complexified general relativity is not a free field theory, but is a theory that describes a linearized self-dual connection propagating on an arbitrary anti-self-dual background. This theory is quantized in the loop representation and, as in the full theory, an infinite dimnensional space of exact solutions to the constraint is found. An inner product is also proposed. The path integral is constructed from the Hamiltonian theory and the measure is explicitly computed nonperturbatively, without relying on a semiclassical expansion. This theory could provide the starting point for a new approach to perturbation theory in $G_{Newton}$ that does not rely on a background field expansion and in which full diffeomorphism invariance is satisfied at each order.

14 pages

References in corpus (2)

• Representations of the holonomy algebras of gravity and non-Abelian gauge theories
• Gravitons and Loops

Cited by in corpus (35)

• Actions for Gravity, with Generalizations: A Review
• Link Invariants of Finite Type and Perturbation Theory
• Towards an Anomaly-Free Quantum Dynamics for a Weak Coupling Limit of Euclidean Gravity
• Constraint algebra in LQG reloaded : Toy model of a U(1)^{3} Gauge Theory I
• Constraint algebra in LQG reloaded : Toy model of an Abelian gauge theory - II Spatial Diffeomorphisms
• Spacetime Covariant Form of Ashtekar's Constraints
• On the associativity of 1-loop corrections to the celestial operator product in gravity
• Towards an Anomaly-Free Quantum Dynamics for a Weak Coupling Limit of Euclidean Gravity: Diffeomorphism Covariance
• Finite, diffeomorphism invariant observables in quantum gravity
• The constraint algebra in Smolins' $G\to 0$ limit of 4d Euclidean Gravity
• Quantizing the non-linear graviton
• A real alternative to quantum gravity in loop space
• Hamiltonian dynamics for Einstein's action in G$\to$0 limit
• Hamiltonian dynamics of extended objects: Regge-Teitelboim model
• Euclidean LQG Dynamics: An Electric Shift in Perspective
• On quantum propagation in Smolin's weak coupling limit of 4d Euclidean Gravity
• Propagation in Polymer Parameterised Field Theory
• Reduced Phase Space Approach to the $U(1{)}^3$ model for Euclidean Quantum Gravity
• Covariant Origin of the $U(1{)}^3$ model for Euclidean Quantum Gravity
• The effective dynamics of weak coupling loop quantum gravity
• From topological to parametrized field theory
• The Koslowski- Sahlmann representation: Gauge and diffeomorphism invariance
• Ashtekar variables, self-dual metrics and w-infinity
• Towards quantum gravity with neural networks: Solving the quantum Hamilton constraint of U(1) BF theory
• Towards quantum gravity with neural networks: Solving quantum Hamilton constraints of 3d Euclidean gravity in the weak coupling limit
• Stationary cosmology in group field theory
• Euclidean self-dual gravity: Ashtekar variables without gauge fixing
• Exploring the Tomlin-Varadarajan quantum constraints in $U(1{)}^3$ loop quantum gravity: solutions and the Minkowski theorem
• Geometrical Quantum Time in the $U(1{)}^3$ Model of Euclidean Quantum Gravity
• $T\bar{T}$ deformed scattering happens within matrices
• Canonical Gravity in Degenerate Limit
• Abelian 2+1D Loop Quantum Gravity Coupled to a Scalar Field
• Towards a path integral for the pure-spin connection formulation of gravity
• Consistent and non-consistent deformations of gravitational theories
• Asymptotically flat boundary conditions for the $U(1{)}^3$ model for Euclidean Quantum Gravity