2003/10/27 by Florian Conrady, Carlo Rovelli · 2 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Boundary value problem #Euclidean geometry #Euclidean space #Geometry #Kernel (algebra) #Mathematical analysis #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Pure mathematics #Quantum #Quantum Electrodynamics and Casimir Effect #Quantum gravity #Quantum mechanics #Scalar (mathematics) #Scalar field #Scalar field theory #hep-th
paper · pdf · doi:10.1142/s0217751x04019445
published as Int.J.Mod.Phys. A19 (2004) 4037-4068 · 25 pages, 11 figures
arxiv created 2003/10/27 · openalex publication_date 2004/09/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We investigate the idea of a "general boundary" formulation of quantum field theory in the context of the Euclidean free scalar field. We propose a precise definition for an evolution kernel that propagates the field through arbitrary space–time regions. We show that this kernel satisfies an evolution equation which governs its dependence on deformations of the boundary surface and generalizes the ordinary (Euclidean) Schrödinger equation. We also derive the classical counterpart of this equation, which is a Hamilton–Jacobi equation for general boundary surfaces.