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GR: Gravitation und Relativitätstheorie

GR 6: Quantengravitation – Kanonische Quantisierung, Geometrie, Schrödinger-Newton

GR 6.2: Talk

Friday, March 4, 2005, 17:30–17:45, TU BH262

Effective Action from Geometrical Formulation of Quantum Mechanics — •Aureliano Skirzewski — MPI für Gravitationsphysik, Am Mühlenberg 1, 14476 Golm, Germany

In order to get quantum corrections to the classical equations of motion for an arbitrary system such as a cosmological model, we explore a point of view in which the Hermitian inner product of the Hilbert space of the quantum system induces a symplectic structure and a metric in an infinite dimensional projective space [gr-qc/9706069]. The procedure is suggested when realizing that the quantum phase space is a bundle over the classical one and that the space of functions on this submanifold can be preserved under the action of the quantum Hamiltonian’s vector field once certain assumptions are made. We review the general framework and discuss examples to compare with the ussual effective action’s procedure.