Solution of the noncanonicity puzzle in General Relativity: a new Hamiltonian formulation

Understand

We study the transformation leading from Arnowitt, Deser, Misner (ADM) Hamiltonian formulation of General Relativity (GR) to the $\Gamma\Gamma$ metric Hamiltonian formulation derived from the Lagrangian density which was firstly proposed by Einstein.

• We classify this transformation as gauged canonical - i.e.
• canonical modulo a gauge transformation.
• In such a study we introduce a new Hamiltonian formulation written in ADM variables which differs from the usual ADM formulation mainly in a boundary term firstly proposed by Dirac.