Abstract
The canonical covariant formalism (CCF) of the topological five-dimensional Chern–Simons gravity is constructed. Because this gravity model naturally contains a Gauss–Bonnet term, the extended CCF valid for higher curvature gravity must be used. In this framework, the primary constraint and the total Hamiltonian are found. By using the equations of the CCF, it is shown that the bosonic five-form which defines the total Hamiltonian is a first-class dynamical quantity strongly conserved. In this context the equations of motion are also analyzed. To determine the effective interactions of the model, the toroidal dimensional reduction of the five-dimensional Chern–Simons gravity is carried out. Finally the first-order CCF and the usual canonical vierbein formalism (CVF) are related and the Hamiltonian as generator of time evolution is constructed in terms of the first-class constraints of the coupled system.
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Zandron, O.S. Topological Five-Dimensional Chern–Simons Gravity Theory in the Canonical Covariant Formalism. International Journal of Theoretical Physics 42, 2705–2720 (2003). https://doi.org/10.1023/B:IJTP.0000005980.46888.c9
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DOI: https://doi.org/10.1023/B:IJTP.0000005980.46888.c9