A quantum weak energy inequality for spin-one fields in curved space–time

Fewster, Christopher J.; Pfenning, Michael J.

doi:10.1063/1.1602554

Cited by 88 publications

(132 citation statements)

References 55 publications

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“…In fact, the following theorem holds: Let u, v be distributions on X. If WF(u) + WF(v) (element-wise addition) does not contain a zero cotangent vector in T * X, then the distributional product uv is naturally 30 defined. More generally, for a set of n distributions, if ∑ j WF(u j ) does not contain a zero cotangent vector, then ∏ j u j is defined.…”

Section: Quantum Gravitymentioning

confidence: 99%

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Quantum fields in curved spacetime

2015

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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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Section: Quantum Gravitymentioning

confidence: 99%

“…This yields a satisfactory theory at the level of the algebra A , see e.g. [30,33,74] for details. But it is far from clear how to construct an analog of B I for models with interaction, such as Yang-Mills theory, by proceeding this manner.…”

Section: Yang-mills Fieldsmentioning

confidence: 99%

Quantum fields in curved spacetime

2015

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“…Various authors have suggested employing such effects to sustain exotic spacetime geometries containing wormholes [31] or 'warp drive' bubbles [2]. Such suggestions are, however, severely constrained [23,33] by the existence of bounds, known as quantum inequalities (QIs) or quantum weak energy inequalities (QWEIs) [13,14,16,18,19,20,21,22,24,34] which impose limitations on the magnitude and duration of negative energy densities. To give an example, let ρ(t) ψ be the energy density of the free scalar field 2 measured along an inertial worldline in Minkowski space.…”

Section: Introductionmentioning

confidence: 99%

Quantum Inequalities in Quantum Mechanics

Eveson

Fewster

Verch

2005

Ann. Henri Poincaré

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Abstract. We study a phenomenon occuring in various areas of quantum physics, in which an observable density (such as an energy density) which is classically pointwise nonnegative may assume arbitrarily negative expectation values after quantisation, even though the spatially integrated density remains nonnegative. Two prominent examples which have previously been studied are the energy density (in quantum field theory) and the probability flux of rightwardsmoving particles (in quantum mechanics). However, in the quantum field context, it has been shown that the magnitude and space-time extension of negative energy densities are not arbitrary, but restricted by relations which have come to be known as 'quantum inequalities'. In the present work, we explore the extent to which such quantum inequalities hold for typical quantum mechanical systems. We derive quantum inequalities of two types. The first are 'kinematical' quantum inequalities where spatially averaged densities are shown to be bounded below. Specifically, we obtain such kinematical quantum inequalities for the current density in one spatial dimension (imposing constraints on the backflow phenomenon) and for the densities arising in Weyl-Wigner quantization. The latter quantum inequalities are direct consequences of sharp Gårding inequalities. The second type are 'dynamical' quantum inequalities where one obtains bounds from below on temporally averaged densities. We derive such quantum inequalities in the case of the energy density in general quantum mechanical systems having suitable decay properties on the negative spectral axis of the total energy.Furthermore, we obtain explicit numerical values for the quantum inequalities on the onedimensional current density, using various spatial averaging weight functions. We also improve the numerical value of the related 'backflow constant' previously investigated by Bracken and Melloy. In many cases our numerical results are controlled by rigorous error estimates.

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“…For any free field in a (globally hyperbolic) spacetime, there exist zero-mean-field reference states, called Hadamard states, characterized by welldefined two-point correlators [16,19,25]. Such a reference state allows us to perform normal ordering via the point-splitting approach.…”

Section: Estimation Of Spacetime Perturbationmentioning

confidence: 99%

“…The aim of algebraic quantum field theory is to put quantum field theory on rigorous mathematical footing, while the aim of what might be termed pragmatic quantum field theory is to make experimental predictions [14,15]. Strides toward connecting the two have been made recently [5,[16][17][18][19], and this progress makes the current work possible.…”

Section: Introductionmentioning

confidence: 99%

Quantum estimation of parameters of classical spacetimes

et al. 2017

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We describe a quantum limit to measurement of classical spacetimes. Specifically, we formulate a quantum Cramér-Rao lower bound for estimating the single parameter in any one-parameter family of spacetime metrics. We employ the locally covariant formulation of quantum field theory in curved spacetime, which allows for a manifestly background-independent derivation. The result is an uncertainty relation that applies to all globally hyperbolic spacetimes. Among other examples, we apply our method to detection of gravitational waves with the electromagnetic field as a probe, as in laser-interferometric gravitational-wave detectors. Other applications are discussed, from terrestrial gravimetry to cosmology.

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A quantum weak energy inequality for spin-one fields in curved space–time

Cited by 88 publications

References 55 publications

Quantum fields in curved spacetime

Quantum fields in curved spacetime

Quantum Inequalities in Quantum Mechanics

Quantum estimation of parameters of classical spacetimes

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