Can Hamiltonians be boundary observables in Parametrized Field Theories?

Details Can Hamiltonians be boundary observables in Parametrized Field Theories? Can Hamiltonians be boundary observables in Parametrized Field Theories?

2010-10-12

arxiv.org/abs/1010.2535v3

Class.Quant.Grav.28:105002,2011

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

28 pages, LaTeX, references added, citations clarified, typos corrected

Scientific paper

10.1088/0264-9381/28/10/105002

It has been argued that holography in gravitational theories is related to the existence of a particularly useful Gauss Law that allows energy to be measured at the boundary. The present work investigates the extent to which such Gauss Laws follow from diffeomorphism invariance. We study parametrized field theories, which are a class of diffeomorphism-invariant theories without gravity. We find that the Hamiltonian for parametrized field theories vanishes on shell even in the presence of a boundary and under a variety of boundary conditions. We conclude that parametrized theories have no useful Gauss Law, consistent with the absence of holography in these theories.

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