Gauge theory of Gravity based on the correspondence between the $1^{st}$ and the $2^{nd}$ order formalisms
Abstract
This is a shortened version of an invited talk at the XIII International Workshop "Lie Theory and its Applications in Physics", June 1723, Varna, Bulgaria. A covariant canonical gauge theory of gravity free from torsion is studied. Using a metric conjugate momentum and a connection conjugate momentum, which takes the form of the Riemann tensor, a gauge theory of gravity is formulated, with forminvariant Hamiltonian. By the metric conjugate momenta, a correspondence between the AffinePalatini formalism and the metric formalism is established. For, when the dynamical gravitational Hamiltonian $\tilde{H}_{Dyn}$ does not depend on the metric conjugate momenta, a metric compatibility is obtained from the equation of motions, and the equations of motion correspond to the solution is the metric formalism.
 Publication:

arXiv eprints
 Pub Date:
 August 2018
 arXiv:
 arXiv:1808.01978
 Bibcode:
 2018arXiv180801978B
 Keywords:

 High Energy Physics  Theory;
 General Relativity and Quantum Cosmology
 EPrint:
 5 pages, 1 figure, language improved and typos corrected