Conveners
Loop quantum gravity: Monday block 1
- Cong Zhang ()
- Jerzy Lewandowski (Uniwersytet Warszawski)
Loop quantum gravity: Monday block 2
- Cong Zhang ()
- Jerzy Lewandowski (Uniwersytet Warszawski)
Description
One of the most challenging topics in modern physics is how to unify quantum mechanics and general relativity. Loop quantum gravity is a background independent and non-perturbative approach to tackle this challenge. This session is a comprehensive exploration of all facets of the full theory of loop quantum gravity. We encourage presentations on recent developments in canonical loop quantum gravity, spin foam models, group field theory and other related approaches to quantum gravity. Central to our discussions is the concept of background-independent quantization of various theories of gravity and the emergence of quantum geometry.
Selfdual gravity is a reformulation of general relativity on the phase space of an SL(2,C) gauge theory. As pointed out by Abhay Ashtekar in the mid 1980ies, this reformulation lead to a remarkable simplicity of Hamiltonian GR. Using selfdual variables, the constraints simplify and assume the simplest possible polynomial form. In this talk, I lay out a new non-perturbative lattice approach for...
In loop quantum gravity (LQG), the volume operator plays a crucial role in the study of quantum geometry and quantum dynamics. However, the effect of the volume operator is studied only for some simple cases. In this talk, we introduce a numerical algorithm that can give the matrix elements of the volume operator on arbitrary valent gauge-variant and gauge-invariant spin network states and...
We will present a mathematical formulation of Ashtekar variables using the language of differential topology, aligning as closely as possible with the mathematical description of Yang-Mills theories. This approach illuminates the similarities while highlighting the differences between the two.
Additionally, within this framework, we can properly discuss the imposition of symmetries at the...
We present a systematic approach to the kinematics of quantum-reduced loop gravity, a model originally proposed by Alesci and Cianfrani as an attempt to probe the physical implications of loop quantum gravity. In order to implement the quantum gauge-fixing procedure underlying quantum-reduced loop gravity, we introduce a master constraint operator on the kinematical Hilbert space of loop...
Given a base manifold $M$ and a Lie group $G$, we define $\widetilde{\cal A}_M$ a space of generalized $G$-connections on $M$ with the following properties:
- The space of smooth connections ${\cal A}^\infty_M = \sqcup_\pi {\cal A}^\infty_\pi$ is densely embedded in $\widetilde{\cal A}_M = \sqcup_\pi \widetilde{\cal A}^\infty_\pi$; moreover, in contrast with the usual space of generalized...
