A general worldline quantum inequality

Fewster, Christopher J.

doi:10.1088/0264-9381/17/9/302

Cited by 134 publications

(282 citation statements)

References 24 publications

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“…The work described in this section, conducted with Verch [18] and building on earlier work [8,43], uncovers a circle of connections between stability conditions operating at three different scales: the microscopic (Hadamard condition/microlocal spectrum condition), mesoscopic (QEIs) and macroscopic (thermodynamic stability, expressed by the notion of passivity [40]). Each connection takes the form of a rigorous theorem; the reader should be cautioned, however, that the conclusions and hypotheses of successive links do not match perfectly.…”

Section: Stability At Three Scalesmentioning

confidence: 97%

“…They have since been established for the free Klein-Gordon [22,24,26,38,10,16,8,19,47,20], Dirac [47,17,12], Maxwell [26,37,14] and Proca [14] quantum fields in both flat and curved spacetimes, the RaritaSchwinger field in Minkowski space [49], and also for general unitary positiveenergy conformal field theories in two-dimensional Minkowski space [11]. We will not give a full history of the development of the subject, referring the reader to the recent reviews [9,42].…”

Section: Quantum Energy Inequalitiesmentioning

confidence: 99%

“…We now show how QEIs may be derived from the Hadamard condition, using an argument based on that of [8]. The classical Klein-Gordon field φ obeying ( + m 2 )φ = 0 on spacetime (M, g) has stress-energy tensor…”

Section: From Microscopic To Mesoscopicmentioning

confidence: 99%

“…In addition, let S be a convex set of states of A which is closed under operations in O. 8 The energy density ̺(t, x) is assumed to obey:…”

Section: From Mesoscopic To Macroscopicmentioning

confidence: 99%

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Quantum Energy Inequalities and Stability Conditions in Quantum Field Theory

Fewster

2007

Rigorous Quantum Field Theory

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Summary. We give a brief review of quantum energy inequalities (QEIs) and then discuss two lines of work which suggest that QEIs are closely related to various natural properties of quantum field theory which may all be regarded as stability conditions. The first is based on joint work with Verch, and draws connections between microscopic stability (microlocal spectrum condition), mesoscopic stability (QEIs) and macroscopic stability (passivity). The second direction considers QEIs for a countable number of massive scalar fields, and links the existence and scaling properties of QEIs to the spectrum of masses. The upshot is that the existence of a suitable QEI with polynomial scaling is a sufficient condition for the model to satisfy the Buchholz-Wichmann nuclearity criterion. We briefly discuss on-going work with Ojima and Porrmann which seeks to gain a deeper understanding of this relationship.

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Section: Stability At Three Scalesmentioning

confidence: 97%

Section: Quantum Energy Inequalitiesmentioning

confidence: 99%

Section: From Microscopic To Mesoscopicmentioning

confidence: 99%

“…In addition, let S be a convex set of states of A which is closed under operations in O. 8 The energy density ̺(t, x) is assumed to obey:…”

Section: From Mesoscopic To Macroscopicmentioning

confidence: 99%

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Quantum Energy Inequalities and Stability Conditions in Quantum Field Theory

Fewster

2007

Rigorous Quantum Field Theory

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“…Since φ [F T ] = φ ( f T ) (see (10)), this means that the Hawking radiation flux measured by a distant detector is highly entangled with field observables 15 Negative energy fluxes of stress-energy or negative energy densities can occur in quantum field theory even for fields that classically satisfy the dominant energy condition, see e.g. [32,34]. 16 Of course, the approximate description leading to this prediction should be valid only when M M P , where M P denotes the Planck mass (∼ 10 −5 gm), but modifications to the evaporation process at this stage (including the possibility of Planck mass remnants) would not significantly alter the discussion below.…”

Section: C) Hawking Effectmentioning

confidence: 99%

Quantum Fields in Curved Spacetime

Hollands¹,

Wald²

2015

General Relativity and Gravitation

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We review the theory of quantum fields propagating in an arbitrary, classical, globally hyperbolic spacetime. Our review emphasizes the conceptual issues arising in the formulation of the theory and presents known results in a mathematically precise way. Particular attention is paid to the distributional nature of quantum fields, to their local and covariant character, and to microlocal spectrum conditions satisfied by physically reasonable states. We review the Unruh and Hawking effects for free fields, as well as the behavior of free fields in deSitter spacetime and FLRW spacetimes with an exponential phase of expansion. We review how nonlinear observables of a free field, such as the stress-energy tensor, are defined, as well as timeordered-products. The "renormalization ambiguities" involved in the definition of time-ordered products are fully characterized. Interacting fields are then perturbatively constructed. Our main focus is on the theory of a scalar field, but a brief discussion of gauge fields is included. We conclude with a brief discussion of a possible approach towards a nonperturbative formulation of quantum field theory in curved spacetime and some remarks on the formulation of quantum gravity. Quantum field theory in curved spacetime (QFTCS) is the theory of quantum fields propagating in a background, classical, curved spacetime (M , g). On account of its classical treatment of the metric, QFTCS cannot be a fundamental theory of nature. However, QFTCS is expected to provide an accurate description of quantum phenomena in a regime where the effects of curved spacetime may be significant, but effects of quantum gravity itself may be neglected. In particular, it is expected that QFTCS should be applicable to the description of quantum phenomena occurring in the early universe and near (and inside of) black holesprovided that one does not attempt to describe phenomena occurring so near to singularities that curvatures reach Planckian scales and the quantum nature of the spacetime metric would have to be taken into account.It should be possible to derive QFTCS by taking a suitable limit of a more fundamental theory wherein the spacetime metric is treated in accord with the principles of quantum theory. However, this has not been done-except in formal and/or heuristic ways-simply because no present quantum theory of gravity has been developed to the point where such a well defined limit can be taken. Rather, the framework of QFTCS that we shall describe in this review has been obtained by suitably merging basic principles of classical general relativity with the basic principles of quantum field theory in Minkowski spacetime. As we shall explain further below, the basic principles of classical general relativity are relatively easy to identify and adhere to, but it is far less clear what to identify as the "basic principles" of quantum field theory in Minkowski spacetime. Indeed, many of the concepts normally viewed as fundamental to quantum field theory in Minkowski spacetime, such as Poinca...

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Topological censorship and chronology protection

Friedman¹,

Higuchi²

2006

Ann. Phys.

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Over the past two decades, substantial efforts have been made to understand the way in which physics enforces the ordinary topology and causal structure that we observe, from subnuclear to cosmological scales. We review the status of topological censorship and the topology of event horizons; chronology protection in classical and semiclassical gravity; and related progress in establishing quantum energy inequalities.Comment: Dedicated to Rafael Sorkin, whose tutoring and friendship from third grade on is responsible for one of us (JF) having spent his adult life in physics and whose work has inspired both of us. In v.2, some references are updated, and references are added to early work on 2+1 spacetimes and to work on event-horizon topolog

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A general worldline quantum inequality

Cited by 134 publications

References 24 publications

Quantum Energy Inequalities and Stability Conditions in Quantum Field Theory

Quantum Energy Inequalities and Stability Conditions in Quantum Field Theory

Quantum Fields in Curved Spacetime

Topological censorship and chronology protection

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