Related papers: A Lorentz-Covariant Connection for Canonical Gravi…
We study the Dirac-Maxwell model quantized in the Lorenz gauge. In this gauge, the space of quantum mechanical state vectors inevitably be an indefinite metric vector space so that the canonical commutation relation (CCR) is realized in a…
We present a Lagrangian theory of gravitation that develops some ideas proposed several years ago. It is formulated on the 10-dimensional space $\mathcal{S}$ of the local Lorentz frames (tetrads) and it is covariant under the symplectic…
A discussion is given of recent developments in canonical gravity that assimilates the conformal analysis of gravitational degrees of freedom. The work is motivated by the problem of time in quantum gravity and is carried out at the metric…
A formulation of Covariant Canonical Quantization is discussed, which works on an extended Hilbert space and reduces to conventional canonical quantization when constraining to the solution of the field equation a priori. From the formal…
A detailed canonical treatment of a new action for a nonrelativistic particle coupled to background gravity, recently given by us, is performed both in the Lagrangian and Hamiltonian formulations. The equation of motion is shown to satisfy…
We obtain a Lorentz covariant wave equation whose complex wave function transforms under a Lorentz boost according to the following rule, $\Psi(x)\rightarrow e^{\frac{i}{\hbar}f(x)}\Psi(x)$. We show that the spacetime dependent phase $f(x)$…
A simple model is constructed which allows to compute modified dispersion relations with effects from loop quantum gravity. Different quantization choices can be realized and their effects on the order of corrections studied explicitly. A…
In a recent paper [1] we have constructed the spin and tensor representations of SO(4) from which the invariant weight can be derived for the Barrett-Crane model in quantum gravity. By analogy with the SO(4) group, we present the…
The Covariant Canonical Gauge theory of Gravity is generalized by including at the Lagrangian level all possible quadratic curvature invariants. In this approach, the covariant Hamiltonian principle and the canonical transformation…
Spherically symmetric models of loop quantum gravity have been studied recently by different methods that aim to deal with structure functions in the usual constraint algebra of gravitational systems. As noticed by Gambini and Pullin, a…
We study some physical consequences of the introduction of a Lorentz-violating modification term in the linearized gravity, which leads to modified dispersion relations for gravitational waves in the vacuum. We discuss two possible…
We explore the interplay of matter with quantum gravity with a preferred frame to highlight that the matter sector cannot be protected from the symmetry-breaking effects in the gravitational sector. Focusing on Abelian gauge fields, we show…
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…
The covariant phase space formalism in general relativity is a covariant method for constructing the symplectic two-form, Hamiltonian and other conserved charges on the phase space of solutions to the Einstein equation with classical…
We write down the Poisson structure for a relativistic particle where the Lorentz group does not act canonically, but instead as a Poisson-Lie group. In so doing we obtain the classical limit of a particle moving on a noncommutative space…
Covariant classical particle dynamics is described, and the associated covariant relativistic particle quantum mechanics is derived. The invariant symmetric bracket is defined on the space of quantum amplitudes, and its relation to a…
The basics of teleparallel gravity and its extensions are reviewed with particular emphasis on the problem of Lorentz-breaking choice of connection in pure-tetrad versions of the theories. Various possible ways to covariantise such models…
We study the euclidean covariant loop-quantum-gravity vertex numerically, using a cylindrically symmetric boundary state and a convenient value of the Barbero-Immirzi parameter. We show that a classical geometry emerges already at low spin.…
We consider gravity in 2+1 space-time dimensions, with negative cosmological constant and a `Barbero-Immirzi' (B-I) like parameter, when the space-time topology is of the form $ T^2 \times \mathbbm{R}$. The phase space structure, both in…
Poisson bracket relations for generators of canonical transformations are derived directly from the Galilei and Poincar\'e groups of changes of space-time coordinates. The method is simple but rigorous. The meaning of each step is clear…