Generalized Tomonaga-Schwinger equation from the Hadamard formula

Abstract

A generalized Tomonaga--Schwinger equation, holding on the entire boundary of a {\em finite} spacetime region, has recently been considered as a tool for studying particle scattering amplitudes in background-independent quantum field theory. The equation has been derived using lattice techniques under assumptions on the existence of the continuum limit. Here I show that in the context of continuous euclidean field theory the equation can be directly derived from the functional integral formalism, using a technique based on Hadamard's formula for the variation of the propagator.

arXiv comment11 pages, no figures

References in corpus (3)

• A "general boundary" formulation for quantum mechanics and quantum gravity
• Minkowski vacuum in background independent quantum gravity
• Schroedinger's cat and the clock: Lessons for quantum gravity

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