Related papers: The Role of Time Gauge in Quantizing Gravity
After recalling the differential geometry of non-metric connections in the formalism of differential forms, we introduce the idea of a Non-Metricity (NM) connection, whose connection $1$--forms coincides with the non-metricity $1$--forms…
The Plebanski formulation of complex general relativity is given in terms of variables valued in the complexification of the $so(3)$ Lie algebra. Therefore, it is genuinely a gauge theory that is also diffeomorphism-invariant. For this…
We study the Hamiltonian formulation of the generally covariant theory defined by the Lagrangian 4-form L=e_I e_J F^{IJ}(\omega) where e^I is a tetrad field and F^{IJ} is the curvature of a Lorentz connection \omega^{IJ}. This theory can be…
We demonstrate that Einstein's general relativity theory arises as a special case in the framework of the Poincar\'e gauge theory of gravity under the assumption of a suitable nonminimal coupling of matter to the Riemann-Cartan geometry of…
An approach to the quantization of gravity in the presence matter is examined which starts from the classical Einstein-Hilbert action and matter approximated by "point" particles minimally coupled to the metric. Upon quantization, the…
We make a critical review of the semiclassical interpretation of quantum cosmology and emphasise that it is not necessary to consider that a concept of time emerges only when the gravitational field is (semi)classical. We show that the…
The Hamiltonian formulation of scalar-tensor theories of gravity is derived from their Lagrangian formulation by Hamiltonian analysis. The Hamiltonian formalism marks off two sectors of the theories by the coupling parameter $\omega(\phi)$.…
For various theories, in particular gauge field theories, the algebraic form of the Hamiltonian simplifies considerably if one writes it in terms of certain complex variables. Also general relativity when written in the new canonical…
We consider a specific Hamiltonian formulation of the Teleparallel Equivalent of General Relativity, where the canonical variables are expressed by means of differential forms. We show that some ``position'' variables of this formulation…
It's widely recognized that general relativity emerges if we impose invariance under local translations and local Lorentz transformations. In the same manner supergravity arises when we impose invariance under local supersymmetry. In this…
We propose an unified approach to loop quantum gravity and Fedosov quantization of gravity following the geometry of double spacetime fibrations and their quantum deformations. There are considered pseudo-Riemannian manifolds enabled with…
Hamiltonian gravity, relying on arbitrary choices of "space," can obscure spacetime symmetries. We present an alternative, manifestly spacetime covariant formulation that nonetheless distinguishes between "spatial" and "temporal" variables.…
We review the classical formulation of general relativity as an SL(2,C) gauge theory in terms of Ashtekar's selfdual variables and reality conditions for the spatial metric (RCI) and its evolution (RCII), and we add some new observations…
We study a generalized version of the Hamiltonian constraint operator in nonperturbative loop quantum gravity. The generalization is based on admitting arbitrary irreducible SU(2) representations in the regularization of the operator, in…
We develop an effective framework for the $\bar\mu$ scheme of holonomy corrections motivated by loop quantum gravity for vacuum spherically symmetric space-times. This is done by imposing the areal gauge in the classical theory, and then…
We describe a class of modified gravity theories that deform general relativity in a way that breaks time reversal invariance and, very mildly, locality. The algebra of constraints, local physical degrees of freedom, and their linearized…
A gauge theory of quantum gravity is formulated, in which an internal, field dependent metric is introduced which non-linearly realizes the gauge fields on the non-compact group $SL(2,C)$, while linearly realizing them on $SU(2)$.…
We establish the Hamiltonian formulation of the teleparallel equivalent of general relativity, without fixing the time gauge condition, by rigorously performing the Legendre transform. The time gauge condition, previously considered,…
Change and local spatial variation are missing in canonical General Relativity's observables as usually defined, part of the problem of time. Definitions can be tested using equivalent formulations, non-gauge and gauge, because they must…
A generalized quantization principle is considered, which incorporates nontrivial commutation relations of the components of the variables of the quantized theory with the components of the corresponding canonical conjugated momenta…