Linearized dynamics from the 4simplex Regge action
Abstract
We study the relation between the Hessian matrix of the Riemannian Regge action on a 4simplex and linearized quantum gravity. We give an explicit formula for the Hessian as a function of the geometry, and show that it has a single zero mode. We then use a 3D lattice model to show that (i) the zero mode is a remnant of the continuum diffeomorphism invariance, and (ii) we recover the complete free graviton propagator in the continuum limit. The results help clarify the structure of the boundary state needed in the recent calculations of the graviton propagator in loop quantum gravity, and, in particular, its role in fixing the gauge.
 Publication:

Physical Review D
 Pub Date:
 November 2007
 DOI:
 10.1103/PhysRevD.76.104020
 arXiv:
 arXiv:0707.4513
 Bibcode:
 2007PhRvD..76j4020D
 Keywords:

 04.60.Nc;
 04.60.Pp;
 Lattice and discrete methods;
 Loop quantum gravity quantum geometry spin foams;
 General Relativity and Quantum Cosmology;
 High Energy Physics  Lattice
 EPrint:
 16 (+9 Appendix) pages, 1 figure