Télécharger La thèse :

Titre: On the Hamiltonian Formalism of the Einstein-Cartan Gravity with Fermionic Matter

Domaine: Sciences de la matière (SM)

Filière: Physique


Auteur: LAGRAA Meriem Hadjer

Soutenu (e) le: 19/04/2018

Sous la direction de: LAGRAA Mohammed, Professeur, Université Oran 1

Le président du jury : TAHIRI Mohamed, Professeur, Université Oran 1

Examinateur1: ABDESSELAM Boucif, Professeur, Centre Universitaire de Aïn Témouchent

Examinateur2: BALASKA Smaïn, Professeur, Université Oran 1

Examinateur3: BOUDA Ahmed, Professeur, Université de Béjaïa

Examinateur4: NOUICER Khireddine, Professeur, Université de Jijel

Mention: Très Honorable


This thesis presents a detailed analysis of the formalism Hamiltonian of the tetrad-connection Gravity at d-dimension without decomposing the tangent space of the space-time manifold by the ADM decomposition. To avoid the problematic constraints in the Hamiltonian treatment of the theory, we decompose the connection into dynamical and non-dynamical parts, and fix the non-dynamical part to zero. The application of the Dirac procedure with this fixing has allowed to obtain a covariant formalism under the Lorentz transformations and an algebra of first-class constraints closing on structure constants rather than the usual structure functions resulting from the ADM decomposition. The Dirac brackets deliver the same algebra of the first-class constraints, while the second-class ones are eliminated by the strong equality. At the end, we obtain the same physical degrees of freedom of the theory of General Relativity. The Hamiltonian analysis is also performed when Gravity is coupled to fermionic matter. The obtained results establish an algebra of first-class constraints closing on structure constants as the case of pure Gravity. We also obtain, by canonical transformations, a new reduced Phase space equipped with canonical Dirac brackets leading to the same algebra of first-class constraints.

Mots clefs: Tetrad-Connection Gravity; Hamiltonian Formalism; Einstein-Cartan Theory; Spin-connection Projection; Algebra of First-class Constraints; Gravity Constraints; Dirac Brackets; Dirac Quantification Program; Dirac Spinors; Fermions and Gravity.

Publications associées à la thèse

Article 1:

Titre: On the Hamiltonian formalism of the tetrad-connection gravity

Revue: Classical and Quantum Gravity

Référence: Class. Quantum Grav. 34 (2017) 115010 (1-25pp)

Date: 19 Mai 2017