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Localization and the interface between quantum mechanics, quantum field theory and quantum gravity. II: The search of the interface between QFT and QG. (English) Zbl 1228.81045

Summary: The main topics of this second part of a two-part essay ( for Part I see [ibid. 41, No. 2, 104–127 (2010; Zbl 1228.81046)]) 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.

MSC:

81P05 General and philosophical questions in quantum theory
81P40 Quantum coherence, entanglement, quantum correlations
81T99 Quantum field theory; related classical field theories
81V17 Gravitational interaction in quantum theory
83C45 Quantization of the gravitational field

Citations:

Zbl 1228.81046
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References:

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