<i>Elements of Quantum Electrodynamics</i>

Akhiezer, A.I.; Berestetskii, V.B.; Shore, Bruce W.

doi:10.1063/1.3047487

Cited by 507 publications

(815 citation statements)

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“…Some other methods for the relativistic FW transformation, in particular, the method proposed in [24,26], based on one variant of the exclusion method developed by Akhiezer, Berestetskii, and Landau [27,28], also lead to correct results in computing terms of the zeroth and first orders in /S 0 . The method used in [29].…”

Section: Comparison Of Results Obtained By Different Methods Of the Smentioning

confidence: 99%

Comparative analysis of direct and “step-by-step” Foldy-Wouthuysen transformation methods

Silenko

2013

Theor Math Phys

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Relativistic methods for the FoldyWouthuysen transformation of the step-by-step type already at the first step give an expression for the Hamilton operator not coinciding with the exact result determined by the Eriksen method. The methods agree for the zeroth and first orders in the Planck constant terms but do not agree for the second and higher-order terms. We analyze the benefits and drawbacks of various methods and establish their applicability boundaries.

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Section: Comparison Of Results Obtained By Different Methods Of the Smentioning

confidence: 99%

Comparative analysis of direct and “step-by-step” Foldy-Wouthuysen transformation methods

Silenko

2013

Theor Math Phys

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“…The problem is that the probability to lose some energy by radiating photons of energy ω in the interval dω is of order (2α/3π)( q 2 T /m 2 )(dω/ω) [35], where q T is the transverse momentum of the outgoing proton of mass m. Therefore the cross section for pp → (pγ) + (pγ), which may mimic a missing-mass event, is about dσ dy y=0 ∼ 2α 3π…”

Section: Gluon Factorymentioning

confidence: 99%

Double-diffractive processes in high-resolution missing-mass experiments at the Tevatron

2001

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We evaluate, in a model-independent way, the signal-to-background ratio for Higgs→ bb detection in exclusive double-diffractive events at the Tevatron and the LHC. For the missing-mass approach to be able to identify the Higgs boson, it will be necessary to use a central jet detector and to tag b quark jets. The signal is predicted to be very small at the Tevatron, but observable at the LHC. However we note that the background, that is double-diffractive dijet production, may serve as a unique gluon factory. We also give estimates for the double-diffractive production of χ c and χ b mesons at the Tevatron. We emphasize that a high-resolution missing-mass measurement, on its own, is insufficient to identify rare processes.

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“…Although the photon wave function in coordinate representation was introduced already in 1930 by Landau and Peierls [1] the concept was found to suffer from inherent difficulties that were not overcome during the century (see review [2]). The common explanation presented in textbooks (e.g., [3], [4]) may be summed up as follows: (i) no position operator exists for the photon, (ii) while the position wave function may be localized near a space-time point, the measurable quantities like the electromagnetic field vectors, energy, and the photodetection probability remain spread out due to their non-local relation with the position wave function. However, just before the turn of the century both of these widely-espoused notions were disproved [5], [6] and in the new century a fresh interest in the photon localization problem seems to have been awakened (see, e.g., [7], [8], [9]), meeting the needs of developments in near-field optics, cavity QED, and quantum computing.…”

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Photon localization barrier can be overcome

Saari

Menert

Valtna

2005

Optics Communications

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In contradistinction to a widespread belief that the spatial localization of photons is restricted by a power-law falloff of the photon energy density, I.Bialynicki-Birula [Phys. Rev. Lett. 80, 5247 (1998)] has proved that any stronger -up to an almost exponential -falloff is allowed. We are showing that for certain specifically designed cylindrical one-photon states the localization is even better in lateral directions. If the photon state is built from the so-called focus wave mode, the falloff in the waist cross-section plane turns out to be quadratically exponential (Gaussian) and such strong localization persists in the course of propagation.While quantum electrodynamics (QED) underwent an impressive development and reached its maturity in the middle of the last century, one of its basic conceptsthe photon wave function in free space -was deprived of such fortune. Although the photon wave function in coordinate representation was introduced already in 1930 by Landau and Peierls [1] the concept was found to suffer from inherent difficulties that were not overcome during the century (see review [2]). The common explanation presented in textbooks (e.g., [3], [4]) may be summed up as follows: (i) no position operator exists for the photon, (ii) while the position wave function may be localized near a space-time point, the measurable quantities like the electromagnetic field vectors, energy, and the photodetection probability remain spread out due to their non-local relation with the position wave function. However, just before the turn of the century both of these widely-espoused notions were disproved [5], [6] and in the new century a fresh interest in the photon localization problem seems to have been awakened (see, e.g., [7],[8], [9]), meeting the needs of developments in near-field optics, cavity QED, and quantum computing.I. Bialynicki-Birula writes [6] that the statement "even when the position wave function is strongly concentrated near the origin, the energy wave function is spread out over space asymptotically like r −7/2 " (citation from [4], p. 638) is incorrect and that both wave functions may be strongly concentrated near the origin. He demonstrates, on one hand, that photons can be essentially better localized in space -with an exponential falloff of the photon energy density and the photodetection rates. On the other hand, he establishes -and it is even somewhat startling that nobody has done it earlier -that certain localization restrictions arise out of a mathematical property of the positive frequency solutions which therefore are of a universal character and apply not only to photon states but hold for all particles. More specifically, it has been proven in the Letter [6] for the case of spherically imploding-exploding one-photon wavepacket that the Paley-Wiener theorem allows even at instants of maximal localization only such asymptotic decrease of the modulus of the wave function with the radial distance r that is slower than the linear exponential one, i.e., anything slower than ∼...

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Elements of Quantum Electrodynamics

Cited by 507 publications

References 0 publications

Comparative analysis of direct and “step-by-step” Foldy-Wouthuysen transformation methods

Comparative analysis of direct and “step-by-step” Foldy-Wouthuysen transformation methods

Double-diffractive processes in high-resolution missing-mass experiments at the Tevatron

Photon localization barrier can be overcome

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