Localization and the interface between quantum mechanics, quantum field theory and quantum gravity II (The search of the interface between QFT and QG)
Bert Schroer
December 15, 2009
The main topics of this second part of a two-part essay are some consequences
of the phenomenon of vacuum polarization as the most important physical
manifestation of modular localization. Besides philosophically unexpected
consequences, it has led to a new constructive "outside-inwards approach" in
which the pointlike fields and the compactly localized operator algebras which
they generate only appear from intersecting much simpler algebras localized in
noncompact wedge regions whose generators have extremely mild almost free field
behavior. Another consequence of vacuum polarization presented in this essay is
the localization entropy near a causal horizon which follows a logarithmically
modified area law in which a dimensionless area (the area divided by the square
of dR where dR is the thickness of a light sheet) appears. There are arguments
that this logarithmically modified area law corresponds to the volume law of
the standard heat bath thermal behavior. We also explain the symmetry enhancing
effect of holographic projections onto the causal horizon of a region and show
that the resulting infinite dimensional symmetry groups contain the
Bondi-Metzner-Sachs group.
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