Nonpositivity of the energy density in quantized field theories

Epstein, Henri; Glaser, V.; Jaffe, Arthur

doi:10.1007/bf02749799

Cited by 301 publications

(344 citation statements)

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“…In quantum field theory, the energy-momentum tensor T is a local operator that has non-trivial quantum fluctuations, and local energy conditions do not hold [8]. However, the averaged form has recently been established as a theorem [9][10][11].…”

Section: The Average Null Energy Conditionmentioning

confidence: 99%

Universal bounds on operator dimensions from the average null energy condition

Córdova

Diab

2018

J. High Energ. Phys.

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We show that the average null energy condition implies novel lower bounds on the scaling dimensions of highly-chiral primary operators in four-dimensional conformal field theories. Denoting the spin of an operator by a pair of integers (k,k) specifying the transformations under chiral su(2) rotations, we explicitly demonstrate these new bounds for operators transforming in (k, 0) and (k, 1) representations for sufficiently large k. Based on these calculations, along with intuition from free field theory, we conjecture that in any unitary conformal field theory, primary local operators of spin (k,k) and scaling dimension ∆ satisfy ∆ ≥ max{k,k}. If |k −k| > 4, this is stronger than the unitarity bound.

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Section: The Average Null Energy Conditionmentioning

confidence: 99%

Universal bounds on operator dimensions from the average null energy condition

Córdova

Diab

2018

J. High Energ. Phys.

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“…They may be regarded as local remnants of the spectrum condition, i.e., the Minkowski space requirement that the joint spectrum of the generators P µ of spacetime translations should lie in the future causal cone. 6 …”

Section: Microscopic Stability: the Hadamard Conditionmentioning

confidence: 99%

“…However, as has been known for a long time [6], the WEC (and hence DEC) are violated in quantum field theory. It is easy to give a simple proof in Minkowski space: suppose that ̺ = T ab u a u b , where u a is now a smooth timelike vector field, and let f be a nonnegative smooth function of compact support.…”

Section: Introductionmentioning

confidence: 99%

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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“…lt would be instructive to check out the averaged energy conditions (AWEC, ANEC) [25] for this phase. Matter fields which generate a pre-big-bang phase could therefore be quantum in nature, considering the fact that quantum stress tensors can in principle violate the local energy conditions [26] but may satisfy their global (averaged) versions.…”

Section: Frw-like Eramentioning

confidence: 99%

Scale factor duality and the energy condition inequalities

Kar

1997

Physics Letters B

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We demonstrate, by a simple analysis, that cosmological line elements related by scale factor duality also exhibit a duality with respect to the conserva- Stringy cosmologies (for reviews, see [8], [9] ) have certain characteristic features apart from the symmetry of scale factor duality. Firstly, one does not need to bring in an ad-hoc scalar field to get the necessary inflationary phase. The dilaton field which arises as one of the massless excitations of the string world sheet serves the purpose. Moreover, there exists the notion of a phase termed as pre-big-bang (t < 0) during which we have a rapidly inflating universe with a scale factor generically obeying a pole law ( a(t) = (−t) β ; (β < 0 ). This new phase is expected to end at t = 0 where a FRW evolution (a(t) = t β ; 0 < β < 1) takes over and we finally end up with our universe today. Unfortunately, the transition from the pre-big-bang epoch to the FRW phase is plagued by the presence of a singularity, which, if absent would have solved the problem of singularities in GR, at least, in a cosmological setting. The generic presence of a singularity in the transition epoch which spoils a smooth crossover has been termed as the graceful exit problem in string cosmology [10]. Recently, Rey [11] has claimed that by introducing quantum back reaction it is possible to avoid the graceful exit problem at least within the limits of a two dimensional model like that of CGHS [12]. Whether an extension of this to four dimensions is possible or not is still an open question. On the other hand, a quantum cosmology approach to graceful exit has been advocated in [13]. The low energy effective theory that emerges out of string theory is much like Einstein gravity. The equations are derivable from an action which resembles that of a Brans-Dicke 2 theory with the ω parameter set to −1. Specifically, one has :This is the bosonic sector of the genus-zero, low energy action for closed superstrings in the limit when inverse string tension (or α ′ ) goes to zero. Here, H µνλ is the third-rank antisymmetric tensor field, φ the dilaton field and V contains contributions from the dilaton potential and the cosmological constant. The β function equations which are obtained by imposing quantum conformal invariance in the worldsheet sigma model can be derived from this action by performing appropriate variations.Obviously, there are two frames in which the metrics look very different-the string (Brans-Dicke) and the Einstein frame. These frames are related to each other by a conformal transformation. We shall exclusively work in the string frame.The Einstein-like equations can be written in the form G µν = e 2φ T µν where T µν = T φ µν + T M µν (M denotes matter fields other than the dilaton). These equations are exactly those for Brans-Dicke theory with the parameter ω = −1. One might argue that it is not proper to rewrite the β function equations in an explicit Einstein form because at the level of the worldsheet sigma model g µν , φ or B µν -all have the same status-they ...

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Nonpositivity of the energy density in quantized field theories

Cited by 301 publications

References 1 publication

Universal bounds on operator dimensions from the average null energy condition

Universal bounds on operator dimensions from the average null energy condition

Quantum Energy Inequalities and Stability Conditions in Quantum Field Theory

Scale factor duality and the energy condition inequalities

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