Minkowski vacuum in background independent quantum gravity
Jul, 2003
8 pages
Published in:
- Phys.Rev.D 69 (2004) 064019
e-Print:
- gr-qc/0307118 [gr-qc]
Report number:
- ROMA1-2003-1539,
- AEI-2003-063
Citations per year
Abstract: (arXiv)
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 functional W[f,S] of the field f on a closed 3d surface S that bounds a finite region R of Minkowski spacetime. The dependence of W on S is governed by a local covariant generalization of the Schroedinger equation. Particles' scattering amplitudes that describe experiments conducted in the finite region R --the lab during a finite time-- can be expressed in terms of W. The dependence of W on the geometry of S expresses 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 S. However, the detectors' relative location is still coded in the argument of W, because the geometry of the boundary surface is determined by the boundary value f 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_S>, 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.Note:
- 8 pages, no figures Report-no: ROMA1-2003-1539, AEI-2003-063
- 04.60.Gw
- 04.62.+v
- 04.60.Pp
- quantum gravity
- vacuum state: Minkowski
- spin: foam
- propagator
- Hilbert space
- Schroedinger equation
References(30)
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