Gauge theory of Gravity based on the correspondence between the $1^{st}$ and the $2^{nd}$ order formalisms

David Benisty; Eduardo I. Guendelman; Jurgen Struckmeier

doi:10.1007/978-981-15-7775-8_21

paper

Gauge theory of Gravity based on the correspondence between the $1^{s t}$ and the $2^{n d}$ order formalisms

arXiv:1808.01978 · doi:10.1007/978-981-15-7775-8_21

Abstract

This is a shortened version of an invited talk at the XIII International Workshop "Lie Theory and its Applications in Physics", June 17-23, 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 form-invariant Hamiltonian. By the metric conjugate momenta, a correspondence between the Affine-Palatini formalism and the metric formalism is established. For, when the dynamical gravitational Hamiltonian $H ~_{D y n}$ 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.

5 pages, 1 figure, language improved and typos corrected

Gauge theory of Gravity based on the correspondence between the 1st and the 2nd order formalisms

Abstract

Gauge theory of Gravity based on the correspondence between the $1^{s t}$ and the $2^{n d}$ order formalisms