Related papers: Husain-Kuchar model as a constrained BF theory
We perform the Lorentz-covariant Hamiltonian analysis of two Lagrangian action principles that describe general relativity as a constrained BF theory and that include the Immirzi parameter. The relation between these two Lagrangian actions…
How can we relate the constraint structure and constraint dynamics of the general gauge theory in the Hamiltonian formulation with specific features of the theory in the Lagrangian formulation, especially relate the constraint structure…
Spin foam models of quantum gravity are based on Plebanski's formulation of general relativity as a constrained BF theory. We give an alternative formulation of gravity as BF theory plus a certain potential term for the B-field. When the…
Spin foam models are a new approach to a formulation of quantum gravity which is fully background independent, non-perturbative, and covariant, in the spirit of path integral formulations of quantum field theory. In this thesis we describe…
In Loop Quantum Gravity, tremendous progress has been made using the Ashtekar-Barbero variables. These variables, defined in a gauge-fixing of the theory, correspond to a parametrization of the solutions of the so-called simplicity…
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…
We consider a discrete model of euclidean quantum gravity in four dimensions based on a summation over random simplicial manifolds. The action used is the Einstein-Hilbert action plus an $R^2$-term. The phase diagram as a function of the…
The Hilbert-Palatini (HP) Lagrangian of general relativity being written in terms of selfdual and antiselfdual variables contains Ashtekar Lagrangian (which governs the dynamics of the selfdual sector of the theory on condition that the…
We present a new $BF$-type action for complex general relativity with or without a cosmological constant resembling Plebanski's action, which depends on an SO(3,$\mathbb{C}$) connection, a set of 2-forms, a symmetric matrix, and a 4-form.…
We generalize the de Broglie-Bohm (dBB) formulation of quantum mechanics to the case of quantum gravity (QG) by using the effective action for a QG theory. This is done by replacing the dBB equations of motion with the effective action…
Any approach to pure quantum gravity must eventually face the question of coupling quantum matter to the theory. In the past, several ways of coupling matter to spin foam quantum gravity have been proposed, but the dynamics of the coupled…
The standard formulation of general relativity fails to describe some recent interests in the universe. It impels us to go beyond the standard formulation of gravity. The $f(Q)$ gravity theory is an interesting modified theory of gravity,…
The aim of this article is to understand the role of dust reference fields, often also called clocks, on cosmological perturbations around a flat FLRW universe. We derive the Mukhanov-Sasaki (MS) equation for the Brown-Kuchar (BK) and…
We study a $R^{2}$ model of gravity with torsion in a closed Friedmann-Robertson-Walker universe. The model is cast in Hamiltonian form subtracting from the original Lagrangian the total time derivative of $f_{K}f_{R}$, where $f_{K}$ is…
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 $\omega(\phi)$.…
We present a covariant multisymplectic formulation for the Einstein-Hilbert model of General Relativity. As it is described by a second-order singular Lagrangian, this is a gauge field theory with constraints. The use of the unified…
The quantum Zakharov system is described in terms of a Lagrangian formalism. A time-dependent Gaussian trial function approach for the envelope electric field and the low-frequency part of the density fluctuation leads to a coupled,…
The problem of background independent quantum gravity is the problem of defining a quantum field theory of matter and gravity in the absence of an underlying background geometry. Loop quantum gravity (LQG) is a promising proposal for…
The early Dirac proposal to model the electron as a charged membrane is reviewed. A rigidity term, instead of the natural membrane tension, involving linearly the extrinsic curvature of the worldvolume swept out by the membrane is…
We consider quantum mechanics on constrained surfaces which have non-Euclidean metrics and variable Gaussian curvature. The old controversy about the ambiguities involving terms in the Hamiltonian of order hbar^2 multiplying the Gaussian…