As a preparation for its quantization in the loop formalism, the two-dimensional gravitation model of Jackiw and Teitelboim is analysed in the classical canonical formalism. The dynamics is of pure constraints as is well known. A partial gauge fixing of the temporal type being performed, the resulting second class constraints are sorted out and the corresponding Dirac bracket algebra is worked out. Dirac observables of this classical theory are then calculated.

Five-dimensional Chern-Simons theory with (anti-)de Sitter SO(1,5) or SO(2,4) gauge invariance presents an alternative to general relativity with cosmological constant. We consider the zero modes of its Kaluza-Klein compactification to four dimensions. Solutions with vanishing torsion are obtained in the cases of a spherically symmetric 3-space and of a homogeneous and isotropic 3-space, which reproduce the Schwarzshild-de Sitter and CDM cosmological solutions of general relativity. We also check that vanishing torsion is a stable feature of the solutions.

Abstract:We review some properties of a relativistic classical massless charged particle with 9 spin interacting with an external electromagnetic field. We give in particular a proper definition 10 of kinetic energy and total energy, the latter being conserved when the external field is stationary. 11We find that the particle's velocity may differ from c as a result of the spin -electromagnetic field 12 interaction, without jeopardizing Lorentz invariance.

In this paper we consider a model for gravity in 4-dimensional space-time originally proposed by Chamseddine, which may be derived by dimensional reduction and truncation from a 5-dimensional Chern-Simons theory. Its topological origin makes it an interesting candidate for an easier quantization, e.g., in the Loop Quantization framework. The present paper is dedicated to a classical analysis of the model's properties. Cosmological solutions as well as wave solutions are found and compared with the corresponding solutions of Einstein's General Relativity with cosmological constant.

Abstract:We revisit the classical theory of a relativistic massless charged point particle with spin and interacting with an external electromagnetic field. In particular, we give a proper definition of its kinetic energy and its total energy, the latter being conserved when the external field is stationary. We also write the conservation laws for the linear and angular momenta. Finally, we find that the particle's velocity may differ from c as a result of the spin-electromagnetic field interaction, without jeopardizing Lorentz invariance.