Related papers: Hamiltonian of new general relativity using differ…
In this paper we demonstrate closure of the quantum algebra of Hamiltonian constraints in a theory directly related to a certain sector of general relativity reduced to diagonal variables.
The general uncertainty principle applied to gravity can be implemented as a set of modified Poisson brackets in the canonical formalism. As such, the theory is not canonical and the resulting equations of motion do not lead to a covariant…
Three geometric formulations of the Hamiltonian structure of the macroscopic Maxwell equations are given: one in terms of the double de Rham complex, one in terms of L2 duality, and one utilizing an abstract notion of duality. The final of…
Gauge theories with general covariance are particularly reluctant to quantization. We discuss the example of the Hamiltonian formulation of the relativistic point particle that, despite its apparent simplicity, is of crucial importance…
In a companion paper we introduced a kinematical arena for the discussion of the constraints of canonical quantum gravity in the spin network representation based on Vassiliev invariants. In this paper we introduce the Hamiltonian…
This thesis studies general relativity (GR) using chiral formulations, which take advantage of the decomposition of the four-dimensional Lorentz group into self-dual and anti-self-dual sectors. Within this framework, GR can be expressed…
General relativity is a covariant theory of two transverse, traceless graviton degrees of freedom. According to a theorem of Hojman, Kuchar, and Teitelboim, modifications of general relativity must either introduce new degrees of freedom or…
Various Hamiltonian formulations of f(R) gravity can be found in the literature. Some authors follow the Ostrogradsky treatment of higher derivative theories and introduce as extra variables first order time derivatives of the metric…
We present new second derivative, generally covariant theories of gravity for spherically symmetric spacetimes (general covariance is in the $t-r$ plane) belonging to the class where the spherically symmetric Einstein-Hilbert theory is…
In a first part we propose an introduction to multisymplectic formalisms, which are generalisations of Hamilton's formulation of Mechanics to the calculus of variations with several variables: we give some physical motivations, related to…
In the Hamiltonian formulation of general relativity, Einstein's equation is replaced by a set of four constraints. Classically, the constraints can be identified with the generators of the hypersurface-deformation Lie algebroid (HDA) that…
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…
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…
The Hamiltonian constraint formalism is used to obtain the first explicit complete analysis of non-trivial viable dynamic modes for the Poincar\'e gauge theory of gravity. Two modes with propagating spin-zero torsion are analyzed. The…
Basic principles of the Hamilton approach developed for the metric General Relativity (Einstein`s GR) are discussed. In particular, we derive the Hamiltonian of the metric GR in the explicit form. This Hamiltonian is a quadratic function of…
We analyze some extensions of General Relativity. Within the framework of modified gravity, the Newtonian limit of a class of gravitational actions is discussed on the basis of the corresponding scalar-tensor model. For a generalized…
We develop a new, coordinate-free formulation of Hamiltonian mechanics on the dual of a Lie algebroid. Our approach uses a connection, rather than coordinates in a local trivialization, to obtain global expressions for the horizontal and…
This paper presents nine inconsistency theorems for general relativity theory (GRT), and shows that they ultimately originate from the use of Riemannian curvature and the abandonment of universal invariance (which is stronger than the…
Ordinary differential equations of the first order on the torus have been investigated in detail by H. Poincar\'e and A. Denjoy. The long-standing problem of generalising these results for the equations of the order $k>1$ (or for the…
Phase space of General Relativity is extended to a Poisson manifold by inclusion of the determinant of the metric and conjugate momentum as additional independent variables. As a result, the action and the constraints take a polynomial…