Dirac Quantization of Parametrized Field Theory

Details Dirac Quantization of Parametrized Field Theory Dirac Quantization of Parametrized Field Theory

2006-07-18

arxiv.org/abs/gr-qc/0607068v1

Phys.Rev.D75:044018,2007

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

33 pages

Scientific paper

10.1103/PhysRevD.75.044018

Parametrized field theory (PFT) is free field theory on flat spacetime in a diffeomorphism invariant disguise. It describes field evolution on arbitrary foliations of the flat spacetime instead of only the usual flat ones, by treating the `embedding variables' which describe the foliation as dynamical variables to be varied in the action in addition to the scalar field. A formal Dirac quantization turns the constraints of PFT into functional Schrodinger equations which describe evolution of quantum states from an arbitrary Cauchy slice to an infinitesimally nearby one.This formal Schrodinger picture- based quantization is unitarily equivalent to the standard Heisenberg picture based Fock quantization of the free scalar field if scalar field evolution along arbitrary foliations is unitarily implemented on the Fock space. Torre and Varadarajan (TV) showed that for generic foliations emanating from a flat initial slice in spacetimes of dimension greater than 2, evolution is not unitarily implemented, thus implying an obstruction to Dirac quantization. We construct a Dirac quantization of PFT,unitarily equivalent to the standard Fock quantization, using techniques from Loop Quantum Gravity (LQG) which are powerful enough to super-cede the no- go implications of the TV results. The key features of our quantization include an LQG type representation for the embedding variables, embedding dependent Fock spaces for the scalar field, an anomaly free representation of (a generalization of) the finite transformations generated by the constraints and group averaging techniques. The difference between 2 and higher dimensions is that in the latter, only finite gauge transformations are defined in the quantum theory, not the infinitesimal ones.

Affiliated with

Also associated with

No associations

Rating

Dirac Quantization of Parametrized Field Theory does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Dirac Quantization of Parametrized Field Theory, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Dirac Quantization of Parametrized Field Theory will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-121499