• DOI:10.1103/PhysRevD.69.064019
• Corpus ID: 30190407

Minkowski vacuum in background independent quantum gravity

@article{Conrady2004MinkowskiVI,
  title={Minkowski vacuum in background independent quantum gravity},
  author={Florian Conrady and Luisa Doplicher and Robert Oeckl and Carlo Rovelli and Massimo Testa},
  journal={Physical Review D},
  year={2004},
  volume={69},
  pages={064019}
}

• Florian Conrady, L. Doplicher, +2 authors M. Testa
• Published 30 July 2003
• Physics
• Physical Review D

We consider a local formalism in quantum field theory, in which no reference is made to infinitely extended spacial surfaces, infinite past or infinite future. This can be obtained in terms of a func- tional W(',�) of the field ' on a closed 3d surfacethat bounds a finite region R of Minkowski spacetime. The dependence of W(',�) onis governed by a local covariant generalization of the Schrodinger equation. Particles' scattering amplitudes that describe experiments conducted in the finite region R -the laboratory during a finite time- can be expressed in terms of W(',�). The dependence of W(',�) on the geometry ofexpresses the dependence of the transition amplitudes on the relative location of the particle detectors. In a gravitational theory, background independence implies that W(',�) is independent from �. However, the detectors' relative location is still coded in the argument of W('), because the ge- ometry of the boundary surface is determined by the boundary value ' of the gravitational field. This observation clarifies the physical meaning of the functional W(') defined by non perturbative formulations of quantum gravity, such as the spinfoam formalism. In particular, it suggests a way to derive particles' 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�i , which codes the dynamics, from the Minkowski vacuum |0M i , 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.