Generalized Schroedinger equation in Euclidean field theory

Details Generalized Schroedinger equation in Euclidean field theory Generalized Schroedinger equation in Euclidean field theory

2003-10-27

arxiv.org/abs/hep-th/0310246v1

Int.J.Mod.Phys. A19 (2004) 4037-4068

Physics

High Energy Physics

High Energy Physics - Theory

25 pages, 11 figures

Scientific paper

10.1142/S0217751X04019445

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 spacetime 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) Schroedinger equation. We also derive the classical counterpart of this equation, which is a Hamilton-Jacobi equation for general boundary surfaces.

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