Related papers: SO(4,C)-covariant Ashtekar-Barbero gravity and the…
In the context of Loop Quantum Gravity (LQG), we study the fate of Thiemann complexifier in homogeneous and isotropic FRW cosmology. The complexifier is the dilatation operator acting on the canonical phase space for gravity and generates…
The Kodama state is unique in being an exact solution to all the constraints of quantum gravity that also has a well defined semi-classical interpretation as the quantum version of a classical spacetime, namely de Sitter or anti-de sitter…
We study and compare the spectra of geometric operators (length and area) in the quantum kinematics of two formulations of three-dimensional Lorentzian loop quantum gravity. In the SU(2) Ashtekar-Barbero framework, the spectra are discrete…
The Lagrangian formulation of classical field theories and in particular general relativity leads to a coordinate-free, fully covariant analysis of these constrained systems. This paper applies multisymplectic techniques to obtain the…
A manifestly diffeomorphism invariant extension of Einstein gravity is constructed, which includes singular metrics, and whose ADM formulation is Ashtekar's gravity. The latter is shown to be locally equivalent to the covariant theory. It…
We present a general framework and procedure to derive uncertainty relations for observables of quantum systems in a covariant manner. All such relations are consequences of the positive semidefiniteness of the density matrix of a general…
A generally covariant gauge theory for an arbitrary gauge group with dimension $\geq 3$, that reduces to Ashtekar's canonical formulation of gravity for SO(3,C), is presented. The canonical form of the theory is shown to contain only first…
A crucial property of Weyl gravity is its conformal invariance. It is shown how this gauge symmetry is exactly reflected by the two constraints in the Hamiltonian framework. Since the spatial 3-metric is one of the configuration variables,…
We recast the finite-region analysis of Einstein's equations that underpins the ER=EPR program into the loop quantum gravity (LQG) framework. By translating curvature-energy uncertainty relations into holonomy-flux kinematics, and by…
We formulate quantum mechanics on SO(3) using a non-commutative dual space representation for the quantum states, inspired by recent work in quantum gravity. The new non-commutative variables have a clear connection to the corresponding…
A covariant Hamiltonian description of Palatini's gravity on manifolds with boundary is presented. Palatini's gravity appears as a gauge theory satisfying a constraint in a certain topological limit. This approach allows the consideration…
We study numerically the first order radiative corrections to the self-energy, in covariant loop quantum gravity. We employ the recently developed 'sl2cfoam-next' spinfoam amplitudes library, and some original numerical methods. We analyze…
Quantum integrable systems and their classical counterparts are considered. We show that the symplectic structure and invariant tori of the classical system can be deformed by a quantization parameter $\hbar$ to produce a new (classical)…
A Lorentz and general co-ordinate co-variant form of canonical gravity, using Ashtekar's variables, is investigated. A co-variant treatment due to Crnkovic and Witten is used, in which a point in phase space represents a solution of the…
Motivated by the shape invariance condition in supersymmetric quantum mechanics, we develop an algebraic framework for shape invariant Hamiltonians with a general change of parameters. This approach involves nonlinear generalizations of Lie…
A generalization of General Relativity is studied. The standard Einstein-Hilbert action is considered in the Palatini formalism, where the connection and the metric are independent variables, and the connection is not symmetric. As a result…
We extend our investigation of the IR effects on the local dynamics of matter fields in quantum gravity. Specifically we clarify how the IR effects depend on the change of the quantization scheme: different parametrization of the metric and…
We investigate the consequences of the ambiguity of minimal coupling procedure for Einstein-Cartan gravity with Holst term and fermions. A new insight is provided into the nature and physical relevance of coupling procedures considered…
We analyze Born-Infeld inspired gravity in Palatini formulation in the framework of covariant canonical formalism. We determine covariant Hamiltonian and corresponding equations of motion.
A non-perturbative quantum field theory of General Relativity is presented which leads to a new realization of the theory of Covariant Quantum-Gravity (CQG-theory). The treatment is founded on the recently-identified Hamiltonian structure…