Topological five-dimensional Chern--Simons gravity theory in the canonical covariant formalism
type: Item
instance of: scholarly article
title: Topological five-dimensional Chern--Simons gravity theory in the canonical covariant formalism
zbMATH Open document ID: 1038.83034
author: O. S. Zandron
published in: International Journal of Theoretical Physics
publication date: 2004-02-03T00:00:00Z
review text: The topological five-dimensional Chern-Simons gravity was not previously studied and analyzed in the framework of the group manifold approach for gravity (or supergravity). This powerful method allows one to formulate gauge gravity (or supergravity) theories in any dimension by using only geometrical arguments. The efficiency of the method is made evident when the theory is formulated in more than four dimensions. In this paper, it is shown how the extended canonical covariant formalism (CCF) can be used to describe the dynamics of the topological five-dimensional Chern-Simons gravity. This nonlinear model of gravity contains a Gauss-Bonnet term quadratic in curvature, the usual Einstein term, and a cosmological constant term. From the geometrical Lagrangian density which verifies all the prescriptions of the group manifold approach and by using exterior algebra, the first-order CCF is constructed. This first-order formalism covariant in all its steps allows one to find the equations of motion and the constraints in a very simple way. By means of the toroidal-dimensional reduction process, an U(1) gauge model is obtained, in which the different effective interactions can be analyzed. So, by starting from the five-dimensional Chern-Simons gravity theory which naturally contains a Gauss-Bonnet term, and by using purely geometrical arguments, an interacting model with nonminimal coupling to gravity is constructed. Moreover, the nonlinear interaction modifies the Einstein-Maxwell-dilation theory. This model is more general than the Kaluza-Klein model in which the Gauss-Bonnet term is introduced by hand. On the other hand, the CCF is useful for classical formalisms, but at the quantum level the canonical vierbein formalism (CVF) must be used. In the CVF the Hamiltonian is the true generator of time evolution, therefore the relationship between the CCF and the CVF is also analyzed. By omitting explicit calculation, the true Hamiltonian as generator of time evolutions is g…
Mathematics Subject Classification ID: 83E15
zbMATH DE Number: 2036966
zbMATH Keywords: five-dimensional Chern-Simons gravity
zbMATH Keywords: first-order canonical covariant formalism
zbMATH Keywords: Einstein theory
zbMATH Keywords: Gauss-Bonnet term
zbMATH Keywords: bosonic five-form
zbMATH Keywords: total Hamiltonian
zbMATH Keywords: five-dimensional spin connection
zbMATH Keywords: five-form Lagrangian density toroidal-dimensional reduction process
zbMATH Keywords: vierbein canonical formalism
zbMATH Keywords: Lagrangian density
zbMATH Keywords: space-time decomposition
reviewed by: Serguey M. Pokas
MaRDI profile type: Publication
full work available at URL: b:ijtp.0000005980.46888.c9
OpenAlex ID: W2002611361
DOI: 10.1023/B:IJTP.0000005980.46888.C9
description: scientific article; zbMATH DE number 2036966