Non-canonicity in Arnowitt-Deser-Misner Hamiltonian formulation of General Relativity: a first hint of reference frame in the Canonical Quantization

by Dr Matteo Lulli

Wednesday 20 Apr 2011, 15:00 → 16:00 Europe/Rome

Aula Conversi (Dip. di Fisica - Edificio G. Marconi)

During the last 50 years the Canonical Quantization Programme of General Relativity deeply relied on Arnowitt-Deser-Misner (ADM) Hamiltonian formulation and on its constraints which eventually led to the famous Wheeler-DeWitt equation. Recent results show, however, that ADM Hamiltonian formulation is not linked by a canonical transformation to Dirac's metric Hamiltonian formulation. It is then reasonable that this result could have consequences on the Canonical Quantization of the theory. We will show the latest results on this matter leading to the emergence of a dependence on the gauge choice in the wave functional. The quantization procedure is applied on a new Hamiltonian formulation, expressed in ADM variables, which is canonically related to the metric one.