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• W2891482076 abstract "In a spacetime divided into two regions <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M1><mml:mrow><mml:msub><mml:mrow><mml:mi>U</mml:mi></mml:mrow><mml:mrow><mml:mn mathvariant=normal>1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math> and <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M2><mml:mrow><mml:msub><mml:mrow><mml:mi>U</mml:mi></mml:mrow><mml:mrow><mml:mn mathvariant=normal>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math> by a hypersurface <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M3><mml:mrow><mml:mi mathvariant=normal>Σ</mml:mi></mml:mrow></mml:math>, a perturbation of the field in <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M4><mml:mrow><mml:msub><mml:mrow><mml:mi>U</mml:mi></mml:mrow><mml:mrow><mml:mn mathvariant=normal>1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math> is coupled to perturbations in <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M5><mml:mrow><mml:msub><mml:mrow><mml:mi>U</mml:mi></mml:mrow><mml:mrow><mml:mn mathvariant=normal>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math> by means of the holographic imprint that it leaves on <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M6><mml:mrow><mml:mi mathvariant=normal>Σ</mml:mi></mml:mrow></mml:math>. 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 <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M7><mml:mrow><mml:mi>U</mml:mi></mml:mrow></mml:math> can be calculated integrating (possibly nonlocal) gauge invariant conserved currents on hypersurfaces such that <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M8><mml:mo>∂</mml:mo><mml:mi mathvariant=normal>Σ</mml:mi><mml:mo>⊂</mml:mo><mml:mo>∂</mml:mo><mml:mi>U</mml:mi></mml:math>. 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 <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M9><mml:mo stretchy=false>[</mml:mo><mml:mi mathvariant=normal>Σ</mml:mi><mml:mo stretchy=false>]</mml:mo></mml:math>, and if <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M10><mml:mrow><mml:mi>U</mml:mi></mml:mrow></mml:math> is homeomorphic to a four ball the homology class is determined by its boundary <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M11><mml:mi>S</mml:mi><mml:mo>=</mml:mo><mml:mo>∂</mml:mo><mml:mi mathvariant=normal>Σ</mml:mi></mml:math>. 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 <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M12><mml:mrow><mml:mi>S</mml:mi></mml:mrow></mml:math>. However, nonholographic observables are needed to distinguish between gauge inequivalent solutions." @default.
• W2891482076 created "2018-09-27" @default.
• W2891482076 creator A5024855132 @default.
• W2891482076 date "2019-02-07" @default.
• W2891482076 modified "2023-10-03" @default.
• W2891482076 title "Gauge from Holography and Holographic Gravitational Observables" @default.
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