Minkowski vacuum in background independent quantum gravity
Abstract
We consider a local formalism in quantum field theory, in which no reference is made to infinitely extended spatial surfaces, infinite past or infinite future. This can be obtained in terms of a functional W[φ,Σ] of the field φ on a closed 3D surface Σ that bounds a finite region R of Minkowski spacetime. The dependence of W[φ,Σ] on Σ is governed by a local covariant generalization of the Schrödinger equation. The particle scattering amplitudes that describe experiments conducted in the finite region R—the laboratory during a finite time—can be expressed in terms of W[φ,Σ]. The dependence of W[φ,Σ] on the geometry of Σ expresses the dependence of the transition amplitudes on the relative location of the particle detectors. In a gravitational theory, background independence implies that W[φ,Σ] is independent of Σ. However, the detectors’ relative location is still coded in the argument of W[φ], because the geometry of the boundary surface is determined by the boundary value φ of the gravitational field. This observation clarifies the physical meaning of the functional W[φ] defined by nonperturbative formulations of quantum gravity, such as spinfoam formalism. In particular, it suggests a way to derive the particle scattering amplitudes from a spinfoam model. In particular, we discuss the notion of vacuum in a generally covariant context. We distinguish the nonperturbative vacuum 0_{Σ}>, which codes the dynamics, from the Minkowski vacuum 0_{M}>, which is the state with no particles and is recovered by taking appropriate large values of the boundary metric. We derive a relation between the two vacuum states. We propose an explicit expression for computing the Minkowski vacuum from a spinfoam model.
 Publication:

Physical Review D
 Pub Date:
 March 2004
 DOI:
 10.1103/PhysRevD.69.064019
 arXiv:
 arXiv:grqc/0307118
 Bibcode:
 2004PhRvD..69f4019C
 Keywords:

 04.60.Pp;
 04.60.Gw;
 04.62.+v;
 Loop quantum gravity quantum geometry spin foams;
 Covariant and sumoverhistories quantization;
 Quantum field theory in curved spacetime;
 General Relativity and Quantum Cosmology
 EPrint:
 8 pages, no figures