Analytic Structure of Amplitudes in Gauge Theories With Confinement

Oehme, Reinhard

doi:10.1142/s0217751x95000978

Cited by 60 publications

(138 citation statements)

References 38 publications

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“…We also provide a parameterization of the gluon propagator that is analytic throughout the complex p 2 plane except on the real timelike axis and which decreases to zero in every direction of the complex p 2 plane. Such behavior satisfies the usual axioms of local quantum field theory [10] (except positivity). For the quark propagator, we analyze several general constraints, lattice data [11], and solutions of the coupled quark-gluon-ghost Dyson-Schwinger equations (DSEs) [12].…”

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confidence: 62%

Analytic structure of the gluon and quark propagators in Landau gauge QCD

Alkofer

Detmold

Fischer

et al. 2005

Nuclear Physics B - Proceedings Supplements

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In Landau gauge QCD the infrared behavior of the propagator of transverse gluons can be analytically determined to be a power law from Dyson-Schwinger equations. This propagator clearly shows positivity violation, indicating the absence of the transverse gluons from the physical spectrum, i.e. gluon confinement. A simple analytic structure for the gluon propagator is proposed capturing all important features. We provide arguments that the Landau gauge quark propagator possesses a singularity on the real timelike axis. For this propagator we find a positive definite Schwinger function.The standard model of particle physics consists of gauge field theories. These have been postulated on the basis of symmetries and their elementary excitations do not reflect the observed particle spectrum. In the quantum formulation of these theories, especially in Poincaré-covariant gauges, an intricate problem is posed by the separation of physical and unphysical degrees of freedom.In Quantum Electrodynamics (QED) in linear covariant gauges, the electromagnetic field can be decomposed into transverse, longitudinal and timelike photons, however, only transverse polarizations are observed. From a purely mathematical point of view, this can be understood from the representations of the Poincaré group for massless states: massless particles have only two possible polarizations [1]. The apparent contradiction is resolved by the fact that timelike and longitudinal photons cancel exactly in the S-matrix [2]. In this context we emphasize that the states of quantum gauge field theories in covariant gauges necessarily constitute an indefinite metric space. In covariant gauge QED one thus has to sacrifice the principle of positivity of the representation space. * Summary of a talk given at several occasions; to be published in the proceedings of the international conference QCD DOWN UNDER, March 10 -19, Adelaide, AustraliaIn Quantum Chromodynamics (QCD) in linear covariant gauges, the cancellation of unphysical degrees of freedom in the S-matrix is substantially complicated by the self-interaction of the gauge fields and by the ghost fields that are necessarily present in the quantum formulation of these theories [3]. To order α 2 S in perturbation theory, one obtains amplitudes for the scattering of two transverse gluons into one transverse and one longitudinal gluon. However, at the same order, a ghost loop appears and cancels the various gluon loops, and scattering of transverse to longitudinal gluons does not occur. It is possible to prove this cancellation to all orders in perturbation theory on the basis of the BRS [4] symmetry of the covariantly gauge fixed theory. This symmetry can be represented by gauge transformations with the ghost field as a parameter. The ghost fields, being scalar, anti-commuting fields, are necessarily in the unphysical part of the representation space. In covariant gauge QCD, the physical (and thus positive definite) part of the state space is conjectured to be the set of BRS singlets [5].Gauge fixed QCD is...

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confidence: 62%

Analytic structure of the gluon and quark propagators in Landau gauge QCD

Alkofer

Detmold

Fischer

et al. 2005

Nuclear Physics B - Proceedings Supplements

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“…Such additional singularities could come from so-called anomalous thresholds [145,146], which arise when a hadron is a loosely bound system of other hadronic constituents which can go on-shell (such as is the case of a nucleus in terms of its nucleon constituents), leading to so-called triangular singularities. It was shown that in the case of strong confinement within QCD, the quark-gluon structure of hadrons does not give rise to additional anomalous thresholds [147,148], and the quark singularities are turned into hadron singularities described through an effective field theory. Therefore, the only anomalous thresholds arise for those hadrons which are loosely bound composite systems of other hadrons (e.g., the Σ particle in terms of Λ and π).…”

Section: Fixed-t Dispersion Relationsmentioning

confidence: 99%

Dispersion relations in real and virtual Compton scattering

2003

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A unified presentation is given on the use of dispersion relations in the real and virtual Compton scattering processes off the nucleon. The way in which dispersion relations for Compton scattering amplitudes establish connections between low energy nucleon structure quantities, such as polarizabilities or anomalous magnetic moments, and the nucleon excitation spectrum is reviewed. We discuss various sum rules for forward real and virtual Compton scattering, such as the Gerasimov-Drell-Hearn sum rule and its generalizations, the Burkhardt-Cottingham sum rule, as well as sum rules for forward nucleon polarizabilities, and review their experimental status. Subsequently, we address the general case of real Compton scattering (RCS). Various types of dispersion relations for RCS are presented as tools for extracting nucleon polarizabilities from the RCS data. The information on nucleon polarizabilities gained in this way is reviewed and the nucleon structure information encoded in these quantities is discussed. The dispersion relation formalism is then extended to virtual Compton scattering (VCS). The information on generalized nucleon polarizabilities extracted from recent VCS experiments is described, along with its interpretation in nucleon structure models. As a summary, the physics content of the existing data is discussed and some perspectives for future theoretical and experimental activities in this field are presented.

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“…Here the pion mass is denoted by µ. It has also been shown [4,5] that the underlying confining gauge theory, QCD, does not change the outcome, the proofs for the fixed-t dispersion relations remain valid. The basic requirements for a pion-nucleon analysis are analyticity, crossing and unitarity.…”

Section: C´ν Tµ A´ν Tµmentioning

confidence: 99%