Related papers: Classical Machian Resolution of the Spacetime Reco…
A general quantum constraint of the form $C= - \partial_T^2 \otimes B - I\otimes H$ (realized in particular in Loop Quantum Cosmology models) is studied. Group Averaging is applied to define the Hilbert space of solutions and the relational…
We prove a continuation condition in the context of 3+1 dimensional vacuum Einstein gravity in Constant Mean extrinsic Curvature (CMC) gauge. More precisely, we obtain quantitative criteria under which the physical spacetime can be extended…
We perform, in a manifestly $SO(n-1,1)$ [$SO(n)$] covariant fashion, the Hamiltonian analysis of general relativity in $n$ dimensions written as a constrained $BF$ theory. We solve the constraint on the $B$ field in a way naturally adapted…
The $(3 + 1)$-dimensional (generalized) Dirac equation is shown to have the same form as the equation expressing the condition that a given point lies on a given line in 3-dimensional projective space. The resulting Hamiltonian with a…
We develop a Hamiltonian formulation of the Bianchi type I space-time in conformal gravity, i.e. the theory described by a Lagrangian that is defined by the contracted quadratic product of the Weyl tensor, in a four-dimensional space-time.…
In this review we discuss the connection between two seemingly disparate topics, macroscopic gravity on astrophysical scales and Hamiltonians that are not Hermitian but $PT$ symmetric on microscopic ones. In particular we show that the…
If one replaces the constraints of the Ashtekar-Barbero $SU(2)$ gauge theory formulation of Euclidean gravity by their $U(1)^3$ version, one arrives at a consistent model which captures significant structure of its $SU(2)$ version. In…
Previous work in the literature has studied the Hamiltonian structure of an R-squared model of gravity with torsion in a closed Friedmann-Robertson-Walker universe. Within the framework of Dirac's theory, torsion is found to lead to a…
We investigate a large class of gravity theories that respect spatial covariance, and involve kinetic terms for both the spatial metric and the lapse function. Generally such kind of theories propagate four degrees of freedom, one of which…
Motivated by situations with temporal evolution and spatial symmetries both singled out, we develop a new 2+1+1 decomposition of spacetime, based on a nonorthogonal double foliation. Time evolution proceeds along the leaves of the spatial…
We analyse two principal approaches to the quantization of physical models worked out to date. There are the Faddeev-Popov "heuristic" approach, based on fixing a gauge in the FP path integrals formalism, and the "fundamental" approach by…
The Hamiltonian approach to cosmological perturbations in general relativity in finite space-time is developed, where a cosmological scale factor is identified with spatial averaging the metric determinant logarithm. This identification…
We discuss the Hamiltonian formulation of gravity in 4-dimensional spacetime under Bondi-like coordinates ${v, r, x^a, a=2, 3}$. In Bondi-like coordinates, the 3-dimensional hypersurface is a null hypersurface and the evolution direction is…
We study the Hamiltonian formalism for second order and fourth order nonlinear Schr\"{o}dinger equations. In the case of second order equation, we consider cubic and logarithmic nonlinearities. Since the Lagrangians generating these…
We study the Hamiltonian formulation of Plebanski theory in both the Euclidean and Lorentzian cases. A careful analysis of the constraints shows that the system is non regular, i.e. the rank of the Dirac matrix is non-constant on the…
We propose an exact Hamiltonian lattice theory for (2+1)-dimensional spacetimes with homogeneous curvature. By gauging away the lattice we find a generalization of the ``polygon representation'' of (2+1)-dimensional gravity. We compute the…
In this paper we present a theory of the gravitational field where this field (a kind of square root of g) is represented by a (1,1)-extensor field h describing a plastic distortion of the Lorentz vacuum (a real substance that lives in a…
We present in this paper the formalism for the splitting of a four-dimensional Lorentzian manifold by a set of time-like integral curves. Introducing the geometrical tensors characterizing the local spatial frames induced by the congruence…
The Hamiltonian constraint remains the major unsolved problem in Loop Quantum Gravity (LQG). Seven years ago a mathematically consistent candidate Hamiltonian constraint has been proposed but there are still several unsettled questions…
In this paper, we argue in favor of first-order homogeneous Lagrangians in the velocities. The relevant form of such Lagrangians is discussed and justified physically and geometrically. Such Lagrangian systems possess Reparametrization…