Generalized SCHRÖDINGER Equation in Euclidean Field Theory
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) Schrödinger equation. We also derive the classical counterpart of this equation, which is a HamiltonJacobi equation for general boundary surfaces.
 Publication:

International Journal of Modern Physics A
 Pub Date:
 2004
 DOI:
 10.1142/S0217751X04019445
 arXiv:
 arXiv:hepth/0310246
 Bibcode:
 2004IJMPA..19.4037C
 Keywords:

 11.10.z;
 04.60.Nc;
 04.60.Gw;
 04.60.Pp;
 Field theory;
 Lattice and discrete methods;
 Covariant and sumoverhistories quantization;
 Loop quantum gravity quantum geometry spin foams;
 High Energy Physics  Theory
 EPrint:
 25 pages, 11 figures