Related papers: Spinor Representation for Loop Quantum Gravity
A unified description of all interactions could be based on a higher-dimensional theory involving only spinor fields. The metric arises as a composite object and the gravitational field equations contain torsion-corrections as compared to…
The Hamiltoinian analysis of the vector-tensor theory of gravity is performed. The resulting geometrical dynamics is reformulated into the connection dynamics, with the real SU(2)-connection serving as one of the configuration variables.…
A covariant spin-foam formulation of quantum gravity has been recently developed, characterized by a kinematics which appears to match well the one of canonical loop quantum gravity. In particular, the geometrical observable giving the area…
We analyze the phase space of gravity non-minimally coupled to a scalar field in a generic local Lorentz frame. We reduce the set of constraints to a first-class one by fixing a specific hypersurfaces in the phase space. The main issue of…
Spinors have played an essential but enigmatic role in modern physics since their discovery. Now that quantum-gravitational theories have started to become available, the inclusion of a description of spin in the development is natural and…
We investigate the geometry of the space of N-valent SU(2)-intertwiners. We propose a new set of holomorphic operators acting on this space and a new set of coherent states which are covariant under U(N) transformations. These states are…
Spinorial tools have recently come back to fashion in loop gravity and spin foams. They provide an elegant tool relating the standard holonomy-flux algebra to the twisted geometry picture of the classical phase space on a fixed graph, and…
The role of the modular group in the holonomy representation of (2+1)-dimensional quantum gravity is studied. This representation can be viewed as a "Heisenberg picture", and for simple topologies, the transformation to the ADM…
In a previous work [arXiv:2009.03428] we proposed a new model for Quantum GRavity(QGR) and cosmology, dubbed $SU(\infty)$-QGR. One of the axioms of this model is that Hilbert spaces of the Universe and its subsystems represent $SU(\infty)$…
We develop in a companion article the kinematics of three-dimensional loop quantum gravity in Euclidean signature and with a negative cosmological constant, focusing in particular on the spinorial representation which is well-known at zero…
The most important part of the new spin-foam loop quantum gravity formulation is the map $Y$: $H^{SU(2)} \rightarrow H^{SL(2,C)}$. It was only recently shown that the Y-Map is convergent in spite of the fact that the classical Peter-Weyl…
In this work, it is demonstrated how the kinematical Hilbert space of Loop Quantum Gravity (LQG) can be inferred from the configuration space of BF theories via the imposition of the Hamiltonian constraints. In particular, it is outlined…
We derive a geometric representation of couplings between spin degrees of freedom and gauge fields within the worldline approach to quantum field theory. We combine the string-inspired methods of the worldline formalism with elements of the…
Spinor gravity is a functional integral formulation of gravity based only on fundamental spinor fields. The vielbein and metric arise as composite objects. Due to the lack of local Lorentz-symmetry new invariants in the effective…
The relation between Loop Quantum Gravity (LQG) and tensor network is explored from the perspectives of bulk-boundary duality and holographic entanglement entropy. We find that the LQG spin-network states in a space $\Sigma$ with boundary…
In this paper we discuss a proposal of coherent states for Loop Quantum Gravity. These states are labeled by a point in the phase space of General Relativity as captured by a spin-network graph. They are defined as the gauge invariant…
In this work we investigate the canonical quantization of 2+1 gravity with cosmological constant $\Lambda>0$ in the canonical framework of loop quantum gravity. The unconstrained phase space of gravity in 2+1 dimensions is coordinatized by…
In this work, we extend the so-called typicality approach, originally formulated in statistical mechanics contexts, to $SU(2)$-invariant spin-network states. Our results do not depend on the physical interpretation of the spin network;…
Vielbeins are necessary when coupling General Relativity (GR) to fermionic matter. This enhances the gauge group of GR to include local Lorentz transformations. In view of a reduced phase space formulation of quantum gravity, in this work…
Two sets of spatially diffeomorphism invariant operators are constructed in the loop representation formulation of quantum gravity. This is done by coupling general relativity to an anti- symmetric tensor gauge field and using that field to…