ﻻ يوجد ملخص باللغة العربية
In a spacetime divided into two regions $U_1$ and $U_2$ by a hypersurface $Sigma$, a perturbation of the field in $U_1$ is coupled to perturbations in $U_2$ by means of the holographic imprint that it leaves on $Sigma$. 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 $U$ can be calculated integrating (possibly non local) gauge invariant conserved currents on hypersurfaces such that $partial Sigma subset partial U$. 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 $[Sigma]$, and if $U$ is homeomorphic to a four ball the homology class is determined by its boundary $S = partial Sigma$. 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 $S$. However, non holographic observables are needed to distinguish between gauge inequivalent solutions.
This paper explores construction of gauge (diffeomorphism)-invariant observables in anti de Sitter (AdS) space and the related question of how to find a holographic map providing a quantum equivalence to a boundary theory. Observables are constructed
The relation between manifold topology, observables and gauge group is clarified on the basis of the classification of the representations of the algebra of observables associated to positions and displacements on the manifold. The guiding, physicall
We show that a generalized version of the holographic principle can be derived from the Hamiltonian description of information flow within a quantum system that maintains a separable state. We then show that this generalized holographic principle ent
Observable currents are locally defined gauge invariant conserved currents; physical observables may be calculated integrating them on appropriate hypersurfaces. Due to the conservation law the hypersurfaces become irrelevant up to homology, and the
We show that gravity and matter fields are generically entangled, as a consequence of the local Poincare symmetry. First, we present a general argument, applicable to any particular theory of quantum gravity with matter, by performing the analysis in