Related papers: Hamiltonian reduction of Bianchi Cosmologies
An invariant description of Bianchi Homogeneous (B.H.) 3-spaces is presented, by considering the action of the Automorphism Group on the configuration space of the real, symmetric, positive definite, $3\times 3$ matrices. Thus, the gauge…
We study the homogeneous but anisotropic cosmological models of Bianchi in presence of a massive scalar field using the ADM Hamiltonian formalism. We begin to describe the main steps to find the ADM Hamiltonian of the General Relativity…
We give a pedagogical introduction to the Hamiltonian formalism of general relativity at an advanced undergraduate and graduate levels. After covering the mathematical pre-requisites as well as the $3+1$-decomposition of spacetime, we…
In the framework of the generalized Hamiltonian formalism by Dirac, the local symmetries of dynamical systems with first- and second-class constraints are investigated. For theories with an algebra of constraints of special form (to which a…
In this paper we provide an action related to a certain sector of general relativity where the algebra of Hamiltonian constraints forms a first class system. This action is a Dirac-consistent stand-alone action with two physical degrees of…
Dirac algorithm allows to construct Hamiltonian systems for singular systems, and so contributing to its successful quantization. A drawback of this method is that the resulting quantized theory does not have manifest Lorentz invariance.…
A finite dimensional system with a quadratic Hamiltonian constraint is Dirac quantized in holomorphic, antiholomorphic and mixed representations. A unique inner product is found by imposing Hermitian conjugacy relations on an operator…
We perform the Hamiltonian analysis of general bimetric gravity. We determine four first class constraints that are generators of the diagonal diffeomorphism. We further analyze the remaining constraints and we present an evidence that…
Ashtekar and Samuel have shown that Bianchi cosmological models with compact spatial sections must be of Bianchi class A. Motivated by general results on the symmetry reduction of variational principles, we show how to extend the…
The ADM approach to canonical general relativity combined with Dirac's method of quantizing constrained systems leads to the Wheeler-DeWitt equation. A number of mathematical as well as physical difficulties that arise in connection with…
We study the Hamiltonian structure of tri-gravity and four-gravity in the framework of ADM decomposition of the corresponding metrics. Hence we can deduce the general structure of the constraint system of multi-gravity. We will show it is…
We analyze carefully the problem of gauge symmetries for Bianchi models, from both the geometrical and dynamical points of view. Some of the geometrical definitions of gauge symmetries (=``homogeneity preserving diffeomorphisms'') given in…
Self-consistent Hamiltonian formulation of scalar theory on the null plane is constructed following Dirac method. The theory contains also {\it constraint equations}. They would give, if solved, to a nonlinear and nonlocal Hamiltonian. The…
This letter describes a novel derivation of general relativity by considering the (non)self-consistency of theories whose Hamiltonians are constraints. The constraints, from Hamilton's equations, generate the evolution, while the evolution,…
In her recent work, Dittrich generalized Rovelli's idea of partial observables to construct Dirac observables for constrained systems to the general case of an arbitrary first class constraint algebra with structure functions rather than…
A careful study of the induced transformations on spatial quantities due to 4-dimensional spacetime diffeomorphisms in the canonical formulation of general relativity is undertaken. Use of a general formalism, which indicates the role of…
The Hamiltonian formulation of general relativity (GR) is considered in finite space-time and a specific frame of reference given by the diffeo-invariant components of the Fock simplex in terms of the Dirac -- ADM variables. The evolution…
The two-dimensional effective Polyakov action is often realized as the anomalous contributions of string theories and fermions coupled to gravity in two-dimensions. However, as a result of the reparameterization invariance, one finds that…
In the framework of the generalized Hamiltonian formalism by Dirac, the local symmetries of dynamical systems with first- and second-class constraints are investigated in the general case without restrictions on the algebra of constraints.…
The application of the divergence theorem in a non-coordinated basis is shown to lead to a corrected variational principle for Class B Bianchi cosmological models. This variational principle is used to construct a Hamiltonian formulation…