MG11 
Talk detail
 

 Participant 

Institution

Session

Talk

Abstract

A generalized Schroedinger equation for loop quantum cosmology

A temporally discrete Schroedinger time evolution equation is proposed for isotropic quantum cosmology coupled to a massless scalar source. The approach employs dynamically determined intrinsic time. Possible implementations include simple time stepping or superpositions of Planckian times, reflecting fluctuations arising from an intrinsically fixed lapse function. The semiclassical limit is compared and contrasted with results obtained by Bojowald. The classical foundations of this approach can be found in preprints gr-qc/0503013 and gr-qc/0503014.

Rosenfeld, Bergmann, Dirac and the invention of constrained Hamiltonian dynamics

In a paper appearing in Annalen der Physik in 1930 Leon Rosenfeld invented the first iterative procedure for producing Hamiltonian constraints. He displayed and correctly distinguished the vanishing Hamiltonian generator of time evolution, and the vanishing generator of gauge transformations for general relativity with Dirac electron and electrodynamic field sources. Though he did not do so, had he chosen one of his tetrad fields to be normal to his spacetime foliation, he would have anticipated by almost thirty years the general relativisitic Hamiltonian first written down by Paul Dirac. Peter Bergmann and his coworkers, in addition to Dirac, independently invented and further elaborated constrained Hamiltonian dynamical formalisms in the late 1940’s and 1950’s. It is unclear what if any effect Rosenfeld’s pioneering work had on the full development of the theory that now underlies all canonical approaches to modern gauge theories.