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

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 Higgsand 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 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 solutions of various (Yang–Mills and linear zero-rest-mass) field equations. Thus for these field configurations some ‘classical quasi-local holography’ holds.