摘要：In a spacetime divided into two regions and by a hypersurface , a perturbation of the field in is coupled to perturbations in by means of the holographic imprint that it leaves on . The linearized gluing field equation constrains perturbations on the two sides of a dividing hypersurface, and this linear operator may have a nontrivial null space. A nontrivial perturbation of the field leaving a holographic imprint on a dividing hypersurface which does not affect perturbations on the other side should be considered physically irrelevant. This consideration, together with a locality requirement, leads to the notion of gauge equivalence in Lagrangian field theory over confined spacetime domains. Physical observables in a spacetime domain can be calculated integrating (possibly nonlocal) gauge invariant conserved currents on hypersurfaces such that . The set of observables of this type is sufficient to distinguish gauge inequivalent solutions. The integral of a conserved current on a hypersurface is sensitive only to its homology class , and if is homeomorphic to a four ball the homology class is determined by its boundary . We will see that a result of Anderson and Torre implies that for a class of theories including vacuum general relativity all local observables are holographic in the sense that they can be written as integrals of over the two-dimensional surface . However, nonholographic observables are needed to distinguish between gauge inequivalent solutions.
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