Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2011-01-25
Phys.Rev.D83:105026,2011
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
22+8 pages
Scientific paper
10.1103/PhysRevD.83.105026
To obtain a well defined path integral one often employs discretizations. In the case of gravity and reparametrization invariant systems, the latter of which we consider here as a toy example, discretizations generically break diffeomorphism and reparametrization symmetry, respectively. This has severe implications, as these symmetries determine the dynamics of the corresponding system. Indeed we will show that a discretized path integral with reparametrization invariance is necessarily also discretization independent and therefore uniquely determined by the corresponding continuum quantum mechanical propagator. We use this insight to develop an iterative method for constructing such a discretized path integral, akin to a Wilsonian RG flow. This allows us to address the problem of discretization ambiguities and of an anomaly--free path integral measure for such systems. The latter is needed to obtain a path integral, that can act as a projector onto the physical states, satisfying the quantum constraints. We will comment on implications for discrete quantum gravity models, such as spin foams.
Bahr Benjamin
Dittrich Bianca
Steinhaus Sebastian
No associations
LandOfFree
Perfect discretization of reparametrization invariant path integrals 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 Perfect discretization of reparametrization invariant path integrals, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Perfect discretization of reparametrization invariant path integrals will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-542318