Generalized Schrödinger equation in Euclidean field theory

Conrady, Florian; Rovelli, Carlo

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Generalized Schrödinger equation in Euclidean field theory

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Conrady, Florian
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Conrady, F., & Rovelli, C. (2004). Generalized Schrödinger equation in Euclidean field theory. International Journal of Modern Physics A, 19(24), 4037-4068.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-50CD-4

Abstract

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.