For more information about this meeting, contact Nigel Higson, John Roe, Ping Xu, Mathieu Stienon.
|Title:||Dynamics of constrained quantum systems and reduction|
|Seminar:||Noncommutative Geometry Seminar|
|Speaker:||Artur Tsobanjan, Penn State|
|Several issues arising in canonical quantization of general relativity are most readily studied in homogeneous cosmological models. These models formulated as mechanical systems possess no true Hamiltonian. Instead, their dynamics is governed by the Hamiltonian flow of a so-called 'Hamiltonian constraint' - a real-valued function on the phase-space that, on physical grounds, is constrained to vanish. This structural feature is shared by all time-reparametrization-invariant mechanical systems. True physical degrees of freedom are identified with the symplectic quotient of the phase-space by the action of the group R (time evolution) induced by the Hamiltonian constraint. For the purposes of quantization, working with the quotient space presents several, sometimes prohibitive, technical difficulties and results in the loss of a clear dynamical interpretation of the theory. To avoid these, one typically first quantizes the full phase-space and subsequently attempts to reduce the system post-quantization. In this talk we will look at a method for performing the reduction of quantum systems with a Hamiltonian constraint in the near-classical regime, focusing on the dynamical interpretation.|
Room Reservation Information
|Date:||02 / 24 / 2011|
|Time:||02:30pm - 03:30pm|