The cauchy data space formulation of classical field theory

Abstract

The space C of Cauchy data essentially consists of all Cauchy data on all Cauchy surfaces for the field theory under consideration. There is a canonically defined distribution on C , the integral manifolds of which represent the histories of the field. This formulation of field theory is purely intrinsic in contradistinction to the standard Hamiltonian formulation which requires a 3 + 1 splitting of the space time.