Negative energy densities in integrable quantum field theories at one-particle level

Bostelmann, Henning; Cadamuro, Daniela

doi:10.1103/physrevd.93.065001

Cited by 18 publications

(21 citation statements)

References 28 publications

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“…This effect was first described by Allcock in the context of the arrival time problem in quantum mechanics [1], and then discussed in detail by Bracken and Melloy [2]. More recently, the backflow effect has attracted renewed interest [3][4][5][6][7], partially related to a proposed experiment to measure it [8], and partially because of its connection to other "quantum inequalities" appearing in quantum field theory [3,9] .…”

Section: Introductionmentioning

confidence: 99%

Quantum backflow and scattering

2017

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Backflow is the phenomenon that the probability current of a quantum particle on the line can flow in the direction opposite to its momentum. In this article, previous investigations of backflow, pertaining to interaction-free dynamics or purely kinematical aspects, are extended to scattering situations in short-range potentials. It is shown that backflow is a universal quantum effect which exists in any such potential, and is always of bounded spatial extent in a specific sense. The effects of reflection and transmission processes on backflow are investigated, both analytically for general potentials, and numerically in various concrete examples.Comment: minor changes, as published in Phys. Rev. A; 13 pages, 11 figures, 3 videos, computer cod

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Section: Introductionmentioning

confidence: 99%

Quantum backflow and scattering

2017

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“…Certainly, the fact that the expectation value of the energy density associated with a quantum free scalar field measured on an inertial world line of the Minkowski space-time may be negative becomes relevant since this fact has important implications on a number of aspects of quantum physics, aspects related to quantum field theory being perhaps the most significant ones [5][6][7][8][9][10][11][12][13][14][15]. By theorem 1, we have deduced the minimal value taken on by ( ) p u ; this is a useful condition to be fulfilled by the function ( ) p u whose relevance is clearly manifest.…”

Section: Discussionmentioning

confidence: 99%

Some Theorems upon Negative Energy Density of a Quantum Free Scalar Field in an Inertial World Line of the Minkowski Space-Time

Grado-Caffaro¹

2017

NHMP

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Abstract. After presenting a lemma, two theorems on negative energy density associated with a quantum free scalar field are established. The first theorem provides a lower bound for a non-negative weight function whose existence is guaranteed by the lemma. The above energy density is evaluated over an inertial world line of the Minkowski space-time. The second theorem provides an upper bound for the averaged (with respect to the sampling function) absolute expectation value of the negative energy-density function. In particular, a complex-valued sampling function is introduced by the first time so a more generalized formulation is proposed. IntroductionIn quantum field theory, one can find very interesting examples on negative energy density (see, for instance, ref.[1]). Referring to the general context of quantum physics, there are cases in which energy density can be negative. In this respect, the Casimir effect (see, for example, ref.[1]) is certainly relevant: the quantum fluctuations of the electromagnetic field in the vacuum give rise to a macroscopic effect (Casimir effect) by which the electromagnetic-energy density is negative in the cavity formed by two conducting plates separated by a certain distance. One can think that, in principle, the energy density associated with a quantum field can be made arbitrarily negative at any point of the space-time by choosing a suitable state. Despite considering a classical field in which energy densities are positive in every point of the space-time, the renormalized energy density of the field quantized from the above classical field can be zero and can take either strictly positive or strictly negative values (note that the above density must be continuous). In principle, the renormalized energy density in question may even be made arbitrarily negative at a given point of the space-time. As a matter of fact, arbitrarily negative expectation values of the energy density can be measured after quantization even though the spatially integrated density holds non-negative. The aim of the present paper lies on proving two useful theorems about negative energy density of a free scalar field on an inertial world line of the Minkowski space-time. In this context, we may consider, for example, Dirac or Klein-Gordon fields. On the other hand, a key ingredient in the hypotheses of the above theorems is assuming realistically that the energy density of the aforementioned free scalar field cannot take on negative values arbitrarily. Really, negative energy density is constrained to certain conditions so that the negativeness of the density is not arbitrary; those conditions have been formulated currently by means of quantum inequalities. Before establishing the theorems in question, we will enunciate a lemma which certainly contributes enough to the clarification of the state of the art. In addition, a complex-valued sampling function will be introduced.

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“…Some of these, for example, the sinh-Gordon model [16], can be derived from a classical Lagrangian, and a candidate for the energy density can be computed directly from the Lagrangian. Other models in this class, for example the generalized sinh-Gordon model in Table 1 of [2], are not associated with a Lagrangian, and it is therefore not a priori clear what one should regard as the stress-energy tensor.…”

Section: Qeis In Integrable Systems At One-particle Levelmentioning

confidence: 99%

“…One finds that in certain models with interacting bosons, the energy density can be negative also in states of fixed particle number. Namely, in the class of lower dimensional quantum integrable models, one can find one-particle expectation values with locally negative energy density [3,2]. Hence, negativity of the energy density is more profound in theories with interaction, and existence of QEIs is far from obvious and poses a challenging question.…”

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Energy Inequalities in Interacting Quantum Field Theories

Cadamuro

2020

Progress and Visions in Quantum Theory in View of Gravity

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The classical energy conditions, originally motivated by the Penrose-Hawking singularity theorems of general relativity, are violated by quantum fields. A reminiscent notion of such conditions are the so called quantum energy inequalities (QEIs), which are however not known to hold generally in quantum field theory.Here we present first steps towards investigating QEIs in quantum field theories with self-interaction. IntroductionOne of the fundamental observables both in quantum and in classical field theory is the stress-energy tensor T αβ . It has a special role in general relativity, as the Einstein equations link the curvature of spacetime to the distribution of matter throughout it. Certain positivity conditions on the stress-energy tensor (e.g., the so called "weak energy condition"), which are fulfilled by many classical matter fields, imply severe constraints on exotic spacetime geometries. They also enter the Penrose and Hawking singularity theorems [19], positive mass theorems [22], and Hawking's chronology protection results [18], among many others. However, in quantum field theory (QFT) these energy conditions are violated; the energy density can have negative expectation values. This raises the question whether the energy conditions on the matter in the assumptions of the singularity theorems are compatible with quantum matter, or whether quantum fields allow the existence of "exotic" spacetimes like time machines, wormholes, warp drives. To exclude these scenarios, there must be constraints to the extent in which quantum fields can cause negative energy densities. These constraints are called "Quantum Energy Inequalities" (QEIs). First investigated by Ford [15], they are reminiscent of classical

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Negative energy densities in integrable quantum field theories at one-particle level

Cited by 18 publications

References 28 publications

Quantum backflow and scattering

Quantum backflow and scattering

Some Theorems upon Negative Energy Density of a Quantum Free Scalar Field in an Inertial World Line of the Minkowski Space-Time

Energy Inequalities in Interacting Quantum Field Theories

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