Quasi-local holography and quasi-local mass of classical fields in Minkowski spacetime

Abstract

The 2-surface characterization of special classical radiative Higgs, Yang–Mills and linear zero-rest-mass fields with any spin is investigated. We determine all the zero quasi-local mass Higgs and Yang–Mills field configurations with compact semi-simple gauge groups, and show that they are plane waves (provided the Higgs field is massless and linear) and appropriate generalizations of plane waves (‘Yang–Mills pp-waves’), respectively. A tensor field (generalizing the energy–momentum tensor for the Maxwell field and of the Bel–Robinson tensor for the linearized gravitational field) is found by means of which the pp-wave nature of the solutions of the linear zero-rest-mass field equations with any spin can be characterized equivalently. It is shown that these radiative Yang–Mills and linear zero-rest-mass fields, given on a finite globally hyperbolic domain D, are determined completely by certain unconstrained data set on a closed spacelike 2-surface, the ‘edge of D’. These pure radiative solutions are shown to determine a dense subset in the set of all continuous fields. Thus for these fields some ‘classical quasi-local holography’ holds.