5 research outputs found
Edge States and Entanglement Entropy
It is known that gauge fields defined on manifolds with spatial boundaries
support states localized at the boundaries. In this paper, we demonstrate how
coarse-graining over these states can lead to an entanglement entropy. In
particular, we show that the entanglement entropy of the ground state for the
quantum Hall effect on a disk exhibits an approximate ``area " law.Comment: 16 pages, minor corrections and futher details adde
On a class of 2-surface observables in general relativity
The boundary conditions for canonical vacuum general relativity is
investigated at the quasi-local level. It is shown that fixing the area element
on the 2- surface S (rather than the induced 2-metric) is enough to have a well
defined constraint algebra, and a well defined Poisson algebra of basic
Hamiltonians parameterized by shifts that are tangent to and divergence-free on
$. The evolution equations preserve these boundary conditions and the value of
the basic Hamiltonian gives 2+2 covariant, gauge-invariant 2-surface
observables. The meaning of these observables is also discussed.Comment: 11 pages, a discussion of the observables in stationary spacetimes is
included, new references are added, typos correcte