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 (l.z.r.m) fields with any spin is investigated. We determine all the zero quasi-local mass Higgs- and Yang-Mills field configurations with compact semisimple 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 l.z.r.m. field equations with any spin can be characterized equivalently. It is shown that these radiative Yang-Mills and l.z.r.m. 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 solutions of various (Yang-Mills and l.z.r.m.) field equations. Thus for these field configurations some `classical quasi-local holography' holds.