Related papers: Lecture Notes in Loop Quantum Gravity. LN4: Hamilt…

Among theoretical issues in General Relativity the problem of constructing its Hamiltonian formulation is still of interest. The most of attempts to quantize Gravity are based upon Dirac generalization of Hamiltonian dynamics for system…

It is shown that the Lorentz invariant $f(T)$ gravity, defined by the coframe-connection-multiplier form of the Lagrangian, can be gauge-fixed to the pure coframe form. After clarifying basic aspects of the problem in the Lagrangian…

The connection between the Hamilton and the standard Lagrange formalism is established for a generic Quantum Field Theory with vanishing vacuum expectation values of the fundamental fields. The Effective Actions in both formalisms are the…

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.…

The Hamiltonian formalism of bigravity and massive gravity is studied here for the general form of the interaction potential of two metrics. In the theories equipped with two spacetime metrics it is natural to use the Kuchar approach,…

The kinematics of loop gravity can be given a manifestly Lorentz-covariant formulation: the conventional SU(2)-spin-network Hilbert space can be mapped to a space K of SL(2,C) functions, where Lorentz covariance is manifest. K can be…

In this paper, an attempt is made to represent 5+1 dimensional gravity (via ADM formalism) in terms of the loop constructions introduced by the author in a companion paper. The "momenta" and "velocity" from the earlier paper, which were…

Within loop quantum gravity we construct a coarse-grained approximation for the Einstein-Maxwell theory that yields effective Maxwell equations in flat spacetime comprising Planck scale corrections. The corresponding Hamiltonian is defined…

This note is devoted to the study of Hamiltonian formalism of modified F(R) Horava-Lifshitz theories of gravity that were proposed recently in arXiv:1001.4102[hep-th]. We also study Hamiltonian formulation of the healthy extended…

We give here a field-theoretical derivation of the Hamiltonian of the non-relativistic quantum electrodynamics in the Coulomb gauge using the Lagrange formalism. It leads to the same result as the usual derivation, where one just replaces…

A key problem in the attempt to quantize the gravitational field is the choice of boundary conditions. These are mixed, in that spatial and normal components of metric perturbations obey different sets of boundary conditions. In the…

In the framework of loop quantum cosmology anomaly free quantizations of the Hamiltonian constraint for Bianchi class A, locally rotationally symmetric and isotropic models are given. Basic ideas of the construction in (non-symmetric) loop…

The principle of local covariance which was recently introduced admits a generally covariant formulation of quantum field theory. It allows a discussion of structural properties of quantum field theory as well as the perturbative…

Since there are quantization ambiguities in constructing the Hamiltonian constraint operator in isotropic loop quantum cosmology, it is crucial to check whether the key features of loop quantum cosmology, such as the quantum bounce and…

The conformal equivalence of fourth-order gravity following from a non-linear Lagrangian L(R) to theories of other types is widely known, here we report on a new conformal equivalence of these theories to theories of the same type but with…

After an overview of the physical motivations for studying quantum gravity, we reprint THE FORMAL STRUCTURE OF QUANTUM GRAVITY, i.e. the 1978 Cargese Lectures by Professor B.S. DeWitt, with kind permission of Springer. The reader is…

The quantization of the gravitational field is discussed within the exact uncertainty approach. The method may be described as a Hamilton-Jacobi quantization of gravity. It differs from previous approaches that take the classical…

This work concerns some issues about the interplay of standard and geometric (Hamiltonian) approaches to finite-dimensional quantum mechanics, formulated in the projective space. Our analysis relies upon the notion and the properties of…

Using a Hamiltonian formulation of the spherically symmetric gravity-scalar field theory adapted to flat spatial slicing, we give a construction of the reduced Hamiltonian operator. This Hamiltonian, together with the null expansion…

By considering the Einstein vacuum field equations linearized about the Minkowski metric, the evolution equations for the gauge-invariant quantities characterizing the gravitational field are written in a Hamiltonian form by using a…