Bondi-Metzner-Sachs Symmetry, Holography on Null-surfaces and Area Proportionality of “Light-slice” Entropy

Schroer, Bert

doi:10.1007/s10701-010-9494-3

Cited by 16 publications

(31 citation statements)

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“…Our goals are, however, broader, as we shall make a novel use of the Killing and conformal structure of Schwarzschild spacetime in order to construct rigorously and unambiguously the Unruh state, contemporary in the static region, inside the internal region and on the future event horizon. To this avail, we shall exploit some techniques which in the recent past have been successfully applied to manifolds with Killing horizons, asymptotically flat spacetimes (see also the recent [53]) as well as cosmological backgrounds [14,15,[20][21][22][41][42][43]. Within this respect, it is also important to mention that, although, for different physical goals, a mathematically similar technology was employed in [31] including a proof of the Hadamard property of the relevant states.…”

Section: Introductionmentioning

confidence: 99%

Rigorous construction and Hadamard property of the Unruh state in Schwarzschild spacetime

Dappiaggi¹,

Moretti²,

Pinamonti³

2011

Advances in Theoretical and Mathematical Physics

138

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The discovery of the radiation properties of black holes prompted the search for a natural candidate quantum ground state for a massless scalar field theory on Schwarzschild spacetime, here considered in the Eddington-Finkelstein representation. Among the several available proposals in the literature, an important physical role is played by the so-called Unruh state, which is supposed to be appropriate to capture the physics of a black hole formed by spherically symmetric collapsing matter. Within this respect, we shall consider a massless Klein-Gordon e-print archive: http://lanl.arXiv.org/abs/0907.1034 CLAUDIO DAPPIAGGI ET AL.field and we shall rigorously and globally construct such state, that is on the algebra of Weyl observables localised in the union of the static external region, the future event horizon and the non-static black hole region. Eventually, out of a careful use of microlocal techniques, we prove that the built state fulfils, where defined, the so-called Hadamard condition; hence, it is perturbatively stable, in other words realizing the natural candidate with which one could study purely quantum phenomena such as the role of the back reaction of Hawking's radiation.From a geometrical point of view, we shall make a profitable use of a bulk-to-boundary reconstruction technique which carefully exploits the Killing horizon structure as well as the conformal asymptotic behaviour of the underlying background. From an analytical point of view, our tools will range from Hörmander's theorem on propagation of singularities, results on the role of passive states, and a detailed use of the recently discovered peeling behaviour of the solutions of the wave equation in Schwarzschild spacetime.

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Section: Introductionmentioning

confidence: 99%

Rigorous construction and Hadamard property of the Unruh state in Schwarzschild spacetime

Dappiaggi¹,

Moretti²,

Pinamonti³

2011

Advances in Theoretical and Mathematical Physics

138

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“…The calculation is particular simple in the massless conformal limit of a conserved current. The same limiting behavior which appears in the dimensionless partial charge also shows up as the leading short distance terms in the (also dimensionless) localization entropy [40] which refers to a fuzzy localized operator algebra instead of a single operator (next section).…”

Section: Heisenberg and The Localization-caused Vacuum Polarizationmentioning

confidence: 64%

The Einstein-Jordan conundrum and its relation to ongoing foundational research in local quantum physics

Schroer

2012

EPJ H

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We demonstrate the extraordinary modernity of the 1924/25 "EinsteinJordan fluctuation conundrum", a Gedankenexperiment which led Jordan to his quantization of waves published as a separate section in the famous Born-Heisenberg-Jordan 1926 "Dreimännerarbeit". The thermal nature of energy fluctuations caused by the restriction of the QFT vacuum to a subvolume remained unnoticed mainly because it is not present in QM. In order to understand the analogy with Einstein's fluctuation calculation in a thermal black body system, it is important to expose the mechanism which causes a global vacuum state to become impure on a localized subalgebra of QFT.The present work presents the fascinating history behind this problem which culminated in the more recent perception that "causal localization" leads to thermal manifestations. The most appropriate concept which places this property of QFT into the forefront is "modular localization". These new developments in QFT led to a new access to the existence problem for interacting quantum fields whose solution has remained outside the range of renormalized perturbation theory. It also clarifies open problems about the relation of particles and fields in particular about the incompletely understood crossing property. Last not least it leads to a constructive understanding of integrable versus non-integrable QFTs..

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“…The logarithmic behavior for d=2 split entropy can actually be derived [47] and is well-known to condensed matter physicists. For Jordan's chiral current model used in the E-J conundrum, the entropy can be directly obtained from the isometry with a chiral statistical mechanics model (section 4).…”

Section: Vacuum Polarization Area Lawmentioning

confidence: 99%

“…In that case the two spacelike extensions would account for the dimensionless area factor and the lightlike contribution would be (as in the chiral Jordan model) logarithmic [47] so that the net result is a logarithmically modified area law.…”

Section: Vacuum Polarization Area Lawmentioning

confidence: 99%

“…In contrast to the approximation of the latter in terms of box-quantized finite volume Gibbs states, the split formalism for open subsystems is a part of the (presently computational rather inaccessible) modular localization theory. It is in particular not clear whether the density matrix from the split property leads to a plain dimensionless area law f area/ε 2 24 as in (6) or to a logarithmically modified area law [47]. For chiral conformal theories on the lightray there is a rigorous derivation of the localization entropy for an interval with vacuum attenuation length ε (surface fuzziness) from the well-known linear length l → ∞ behavior (the "one-dimensional volume factor" l).…”

Section: Modular Localization and Its Thermal Manifestationmentioning

confidence: 99%

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Modular localization and the holistic structure of causal quantum theory, a historical perspective

Schroer

2014

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Recent insights into the conceptual structure of localization in QFT ("modular localization") led to clarifications of old unsolved problems. The oldest one is the Einstein-Jordan conundrum which led Jordan in 1925 to the discovery of quantum field theory. This comparison of fluctuations in subsystems of heat bath systems (Einstein) with those resulting from the restriction of the QFT vacuum state to an open subvolume (Jordan) leads to a perfect analogy; the globally pure vacuum state becomes upon local restriction a strongly impure KMS state. This phenomenon of localization-caused thermal behavior as well as the vacuum-polarization clouds at the causal boundary of the localization region places localization in QFT into a sharp contrast with quantum mechanics and justifies the attribute "holstic". In fact it positions the E-J Gedankenexperiment into the same conceptual category as the cosmological constant problem and the Unruh Gedankenexperiment. The holistic structure of QFT resulting from "modular localization" also leads to a revision of the conceptual origin of the crucial crossing property which entered particle theory at the time of the bootstrap S-matrix approach but suffered from incorrect use in the S-matrix settings of the dual model and string theory.The new holistic point of view, which strengthens the autonomous aspect of QFT, also comes with new messages for gauge theory by exposing the clash between Hilbert space structure and localization and presenting alternative solutions based on the use of stringlocal fields in Hilbert space. Among other things this leads to a radical reformulation of the Englert-Higgs symmetry breaking mechanism. Contents 1 Introduction 282 Vacuum polarization, area law 383 Modular localization and its thermal manifestation 424 The E-J conundrum, Jordan's model 545 Particle crossing, on-shell constructions from modular setting 58 PrefaceThe subject of this paper grew out of many discussions about Jordan's discovery of quantum field theory (QFT) which I had with the late Jürgen Ehlers. These conversations focussed in particular on events between the publication of Jordan's thesis on quantum aspects of statistical quantum mechanics in 1924 [1], and his discovery of QFT which was published in one section of the famous 1926 "Dreimännerarbeit" [2] together with Born and Heisenberg. This famous paper was in fact conceived as the second paper on quantum mechanics (QM). The resistance of Born and Heisenberg against Jordan's section has its natural explanation in that these two authors felt that Jordan was burdening the conceptual struggle to understand the new quantum mechanics with something which was even further out. I met Jürgen Ehlers the first time around 1957 at the University of Hamburg when he was Jordan's assistant and played the leading role in Jordan's general relativity seminar. Our paths split, after I wrote my diploma thesis on a topic of particle theory at the time when particle physics moved away from the university to the newly constructed high energy la...

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Bondi-Metzner-Sachs Symmetry, Holography on Null-surfaces and Area Proportionality of “Light-slice” Entropy

Cited by 16 publications

References 50 publications

Rigorous construction and Hadamard property of the Unruh state in Schwarzschild spacetime

Rigorous construction and Hadamard property of the Unruh state in Schwarzschild spacetime

The Einstein-Jordan conundrum and its relation to ongoing foundational research in local quantum physics

Modular localization and the holistic structure of causal quantum theory, a historical perspective

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