Among the various approaches to the quantum gravity challenge, loop quantum gravity proposes a framework for a canonical quantization of general relativity, describing how the 3d geometry evolves in time. It does not require a priori extra dimensions or supersymmetry. It defines spin network states for the quantum geometry directly at the Planck scale, with a discrete spectra of areas and volumes, and computes their transition amplitudes by path integrals inspired from topological field theory, called spinfoam models. This framework is mathematically rigorous but Continue reading

# Tag Archives: Loop Quantum Gravity

# Towards quantum asymptotic flatness

It is of great physical interest to construct a canonical quantization of asymptotically flat spacetimes. The classical phase space variables are subject to delicate boundary conditions at spatial infinity and the first challenge is to construct a quantum kinematics which carries an imprint of these boundary conditions.

This work is one of a series of papers which seeks to construct such a Continue reading

# Continuous symmetries in discrete space?

Violating Lorentz symmetries can be dangerous. A new model assesses this threat in loop quantum gravity.

Discrete space is attractive in quantization attempts of gravity, but it implies the great danger of violating Lorentz transformations. Any approach must show that modifications of symmetries by discrete space are tame enough for predictions to be consistent with continuum low-energy physics. In the CQG paper, Sandipan Sengupta constructs an encouraging model using Continue reading

# Asymptotic flatness and quantum geometry

From the perspective of quantum gravity, the spacetime is smooth only in an effective sense, and is expected to exhibit a discrete structure at suitably small length scales. Within the gauge theoretic formulation of gravity, there are certain kinematical states which provide an elegant realization of such a scenario. These are known as the spin-network states, and are used extensively in certain quantization approaches, e.g. Loop Quantum Gravity (LQG). However, since these states correspond to a spatially discrete quantum geometry, they cannnot be used to capture the notion of a classical spacetime continuum. This leads to a serious obstacle towards a quantization of Continue reading

# Boundary states in higher-dimensional loop quantum gravity

Higher-dimensional Chern-Simons theory appears in the description of isolated horizon boundaries in higher-dimensional General Relativity.

It is a well-known fact that the presence of boundaries (“edges”) leads to the concept of boundary states, which e.g. ensure gauge invariance for parallel transporters ending on the boundary. Most famously, the quantum Hall effect can be explained using such states. In the context of black hole (quantum) physics, boundary states are important since they are microscopic states associated to the horizon of the black hole. Counting such boundary states in agreement with the macroscopic properties of a black hole is thus a good candidate for a microscopic explanation of the Bekenstein-Hawking entropy. This paradigm has been successfully employed in 3+1 dimension in the context of loop quantum gravity, a canonical quantisation of General Relativity. Continue reading