Reduced Phase Space of the first order Einstein Gravity on ${\bf R}\times T^{2}$

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/148318Chern-Simons formulation of the 2+1 dimensional Einstein gravity with negative cosmological constant is investigated when the spacetime has the topology ${\bf R}\times T^{2}$. The physical phase space is shown to be a direct product of two sub-phase spaces having symplectic structures with opposite signs. Each sub-phase space is found to be a non-Hausdorff manifold plus a set of measure zero. Geometrical interpretation of each point in the phase space is also given. A prescription to quantize this phase space is proposed.Latex 11pagesHigh Energy Physics - TheoryReduced Phase Space of the first order Einstein Gravity on ${\bf R}\times T^{2}$text