Generalized TomonagaSchwinger equation from the Hadamard formula
Abstract
A generalized TomonagaSchwinger equation, holding on the entire boundary of a finite spacetime region, has recently been considered as a tool for studying particle scattering amplitudes in backgroundindependent 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.
 Publication:

Physical Review D
 Pub Date:
 September 2004
 DOI:
 10.1103/PhysRevD.70.064037
 arXiv:
 arXiv:grqc/0405006
 Bibcode:
 2004PhRvD..70f4037D
 Keywords:

 04.60.Pp;
 04.60.Gw;
 04.62.+v;
 Loop quantum gravity quantum geometry spin foams;
 Covariant and sumoverhistories quantization;
 Quantum field theory in curved spacetime;
 General Relativity and Quantum Cosmology
 EPrint:
 11 pages, no figures