On the duality condition for quantum fields

Bisognano, J.J.

doi:10.1063/1.522898

Cited by 542 publications

(710 citation statements)

References 10 publications

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“…If, however, the unperturbed background is such that the undeformed entangling surface exhibits rotational symmetry in the transverse space, then this symmetry will be inherent in the path integral representation ofρ 0 . In particular, as shown in [23] (see also [37][38][39][40][41]) in this caseK 0 is identical to the generator of angular evolution around Σ andÛ takes the form…”

Section: Jhep12(2014)179mentioning

confidence: 78%

Entanglement entropy: a perturbative calculation

Rosenhaus

Smolkin

2014

J. High Energ. Phys.

104

192

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We provide a framework for a perturbative evaluation of the reduced density matrix. The method is based on a path integral in the analytically continued spacetime. It suggests an alternative to the holographic and 'standard' replica trick calculations of entanglement entropy. We implement this method within solvable field theory examples to evaluate leading order corrections induced by small perturbations in the geometry of the background and entangling surface. Our findings are in accord with Solodukhin's formula for the universal term of entanglement entropy for four dimensional CFTs.

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Section: Jhep12(2014)179mentioning

confidence: 78%

Entanglement entropy: a perturbative calculation

Rosenhaus

Smolkin

2014

J. High Energ. Phys.

104

192

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“…This happens at small enough momentum, p z UV 1 and p z IR 1. 8 In this regime we match (3.29) with (3.26) and then obtain the consequence of the IR regularity condition on the UV expansion. This matching procedure was introduced in [52]; see also [53,54].…”

Section: Jhep03(2016)033mentioning

confidence: 99%

“…It is given by a thermal state with respect to boost "time" evolution, at a fixed dimensionless temperature (2π) −1 . Though this is an old result of axiomatic QFT [8], only recently this fact has been used to provide general results for the EE of a planar surface in terms of correlation functions. Rosenhaus and Smolkin [9][10][11][12] proposed a simple way to compute the planar EE perturbing with relevant operators.…”

Section: Jhep03(2016)033mentioning

confidence: 99%

Holographic RG flows, entanglement entropy and the sum rule

Casini

Testé

Torroba

2016

J. High Energ. Phys.

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Abstract:We calculate the two-point function of the trace of the stress tensor in holographic renormalization group flows between pairs of conformal field theories. We show that the term proportional to the momentum squared in this correlator gives the change of the central charge between fixed points in d = 2 and in d > 2 it gives the holographic entanglement entropy for a planar region. This can also be seen as a holographic realization of the Adler-Zee formula for the renormalization of Newton's constant. Holographic regularization is found to provide a perfect match of the finite and divergent terms of the sum rule, and it is analogous to the regularization of the entropy in terms of mutual information. Finally, we provide a general proof of reflection positivity in terms of stability of the dual bulk action, and discuss the relation between unitarity constraints, the null energy condition and regularity in the interior of the gravity solution.

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“…They first realized this at a 1965 conference in Baton Rouge 5 , with statistical mechanics of open systems and the role of the KMS property representing the physical side [7]. The study of the relation between modular operator theory and causal localization in LQP started a decade later [19], and its first application consisted in a more profound understanding [20] of the Unruh Gedankenexperiment [21]. The terminology "modular localization" is more recent and marks the beginning of a new constructive strategy in QFT based on the modular aspects of localization of states and algebras [44] [6].…”

Section: A(r) = B(h(r)) a ≡ B(h) = A(r) ⊗ A(r ⊥ )mentioning

confidence: 99%

“…It has been known for a long time that the algebraic structure associated to free fields allows a functorial interpretation in which operator subalgebras of the global algebra B(H) are the functorial images of certain real subspaces of the Wigner space of one-particle wave functions (the famous so-called "second quantization" 19 ), in particular the spacetime localized algebras are the images of localized real subspaces. This means that the issue of localization to some extend can be studied in the simpler form of localized subspaces of the Wigner particle representation space (unitary positive energy representations of the P-group).…”

Section: Modular Localization and Its Thermal Manifestationmentioning

confidence: 99%

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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On the duality condition for quantum fields

Cited by 542 publications

References 10 publications

Entanglement entropy: a perturbative calculation

Entanglement entropy: a perturbative calculation

Holographic RG flows, entanglement entropy and the sum rule

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

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