Related papers: Dynamics for a 2-vertex Quantum Gravity Model
Non-perturbative approaches to quantum gravity call for a deep understanding of the emergence of geometry and locality from the quantum state of the gravitational field. Without background geometry, the notion of distance should entirely…
The search for a quantum theory of gravity is one of the major challenges facing theoretical physics today. While no complete theory exists, a promising avenue of research is the loop quantum gravity approach. In this approach, quantum…
Loop quantum gravity is an approach to quantum gravity that starts from the Hamiltonian formulation in terms of a connection and its canonical conjugate. Quantization proceeds in the spirit of Dirac: First one defines an algebra of basic…
The ingoing and outgoing null expansions associated to a spatial 2-sphere are quantized in the spherically symmetric model of loop quantum gravity. It is shown that the resulting expansion operators are self-adjoint in the kinematical…
By taking the limit that Newton's Gravitational constant tends to zero, the weak coupling loop quantum gravity can be formulated as a $U(1)^3$ gauge theory instead of the original $SU(2)$ gauge theory. In this paper, a parametrization of…
This paper establishes a link between Noncommutative Geometry and canonical quantum gravity. A semi-finite spectral triple over a space of connections is presented. The triple involves an algebra of holonomy loops and a Dirac type operator…
We show that a class of background independent models of quantum spacetime have local excitations that can be mapped to the first generation fermions of the standard model of particle physics. These states propagate coherently as they can…
After a brief review of spin networks and their interpretation as wave functions for the (space) geometry, we discuss the renormalisation of the area operator in loop quantum gravity. In such a background independent framework, we propose…
One of the main results in canonical quantum gravity is the introduction of spin network states as a basis on the space of kinematical states. To arrive at the physical state space of the theory though we need to understand the dynamics of…
The purpose of this contribution is to give an introduction to quantum geometry and loop quantum gravity for a wide audience of both physicists and mathematicians. From a physical point of view the emphasis will be on conceptual issues…
The two surprising features of gravity are (a) the principle of equivalence and (b) the connection between gravity and thermodynamics. Using principle of equivalence and special relativity in the {\it local inertial frame}, one could obtain…
We discuss the relation between coarse-graining and the holographic principle in the framework of loop quantum gravity and ask the following question: when we coarse-grain arbitrary spin network states of quantum geometry, are we…
Quantum graphity is a background independent model for emergent locality, spatial geometry and matter. The states of the system correspond to dynamical graphs on N vertices. At high energy, the graph describing the system is highly…
Quantum gravity is studied nonperturbatively in the case in which space has a boundary with finite area. A natural set of boundary conditions is studied in the Euclidean signature theory, in which the pullback of the curvature to the…
Spin networks in loop quantum gravity provide a kinematical picture of quantum geometry but lack a natural mechanism for dynamical Dirac-type evolution, while the Wheeler--DeWitt equation typically enters only as an imposed constraint. We…
In this work, we study the classical and quantum properties of the unique commutative Lorentz-covariant connection for loop quantum gravity. This connection has been found after solving the second-class constraints inherited from the…
In this paper we establish the existence of the non-perturbative theory of quantum gravity known as quantum holonomy theory by showing that a Hilbert space representation of the QHD(M) algebra, which is an algebra generated by…
Tensor networks provide a powerful tool for studying many-body quantum systems, particularly making quantum simulations more efficient. In this article, we construct a tensor network representation of the spin network states, which…
This thesis, explores the quantum entanglement and evolution through both a geometric and dynamical perspective. The first part focuses on classical phase space and its central role in Hamiltonian mechanics, emphasizing the importance of…
The space of states and operators for a large class of background independent theories of quantum spacetime dynamics is defined. The SU(2) spin networks of quantum general relativity are replaced by labelled compact two-dimensional…