2003/07/30 by Florian Conrady, Luisa Doplicher, Robert Oeckl +3 · 4 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Boundary value problem #Classical mechanics #Covariant transformation #Gravitation #Gravitational field #Loop quantum gravity #Mathematical physics #Minkowski space #Noncommutative and Quantum Gravity Theories #Physics #Propagator #Quantum #Quantum Electrodynamics and Casimir Effect #Quantum field theory #Quantum gravity #Quantum mechanics #Vacuum energy #gr-qc
paper · pdf · doi:10.1103/physrevd.69.064019
published as Phys.Rev. D69 (2004) 064019 · 8 pages, no figures
arxiv created 2003/07/30 · openalex publication_date 2004/03/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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[\ensuremathφ,\ensuremathΣ] of the field \ensuremathφ on a closed 3D surface \ensuremathΣ that bounds a finite region R of Minkowski spacetime. The dependence of W[\ensuremathφ,\ensuremathΣ] on \ensuremathΣ is governed by a local covariant generalization of the Schr"odinger 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[\ensuremathφ,\ensuremathΣ]. The dependence of W[\ensuremathφ,\ensuremathΣ] on the geometry of \ensuremathΣ expresses the dependence of the transition amplitudes on the relative location of the particle detectors. In a gravitational theory, background independence implies that W[\ensuremathφ,\ensuremathΣ] is independent of \ensuremathΣ. However, the detectors' relative location is still coded in the argument of W[\ensuremathφ], because the geometry of the boundary surface is determined by the boundary value \ensuremathφ of the gravitational field. This observation clarifies the physical meaning of the functional W[\ensuremathφ] 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_\ensuremathΣ〉, which codes the dynamics, from the Minkowski vacuum |0M〉, 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.