Spectral representation of lattice gluon and ghost propagators at zero temperature

Dudal, David; Oliveira, Orlando; Roelfs, Martin; Silva, Paulo

doi:10.1016/j.nuclphysb.2019.114912

Cited by 53 publications

(60 citation statements)

References 58 publications

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“…if the superconvergence relation [6,71] dtρ(t) = 0 holds, which forbids a positive spectral function. Let us support this non-positivity of ρ(t) by using (D1) to show that ρ(t) is certainly negative for very large t. This argument can also be found in the Appendix of [5].…”

Section: Field Propagatorssupporting

confidence: 54%

“…In recent years there has been an increasing interest in the properties of the spectral function (Källen-Lehmann density) of two-point correlation functions, especially in non-Abelian gauge theories such as Quantum Chromodynamics (QCD). It was found [1][2][3][4][5], in lattice simulations for the minimal Landau gauge, that the spectral function of the gluon propagator is not non-negative everywhere, which means that there is no physical interpretation for this propagator like there is for the photon propagator in Quantum Electrodynamics (QED). This behaviour of the gluon spectral function is commonly associated with the concept of confinement [6][7][8][9].…”

Section: Introductionmentioning

confidence: 99%

“…This is the Abelian version of the variation(5). For computational purposes, we have also rescaled the b-field.…”

mentioning

confidence: 99%

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Some remarks on the spectral functions of the Abelian Higgs model

et al. 2019

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We consider the unitary Abelian Higgs model and investigate its spectral functions at one-loop order. This analysis allows to disentangle what is physical and what is not at the level of the elementary particle propagators, in conjunction with the Nielsen identities. We highlight the role of the tadpole graphs and the gauge choices to get sensible results. We also introduce an Abelian Curci-Ferrari action coupled to a scalar field to model a massive photon which, like the non-Abelian Curci-Ferarri model, is left invariant by a modified non-nilpotent BRST symmetry. We clearly illustrate its non-unitary nature directly from the spectral function viewpoint. This provides a functional analogue of the Ojima observation in the canonical formalism: there are ghost states with nonzero norm in the BRST-invariant states of the Curci-Ferrari model. * david.dudal@kuleuven.be †

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Section: Field Propagatorssupporting

confidence: 54%

Section: Introductionmentioning

confidence: 99%

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Some remarks on the spectral functions of the Abelian Higgs model

et al. 2019

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“…where q refers now to the energy-component and ρ D is the (nonpositive definite) spectral density defined at real frequencies ω, with → 0 + [65,66]. As D(q) ∼ 1/q 2 in the IR, for the ghost particle we will study the spectral function associated to its dressing function ρ F rather than ρ D , the two being related by [64]. We also note that assuming q 2 ∆(q) → 0 for q 2 → ∞, as required by perturbation theory, implies a modified version of the usual Oehme-Zimmermann superconvergence (OZS) relation [67,68], which now becomes…”

Section: Generalized Spectral Representation and Reconstruction Methodsmentioning

confidence: 99%

Spectral functions of confined particles

2020

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We determine the gluon and ghost spectral functions along with the analytic structure of the associated propagators from numerical data describing gauge correlators at space-like momenta obtained by either solving the Dyson-Schwinger equations or through lattice simulations. Our novel reconstruction technique shows the expected branch cut for the gluon and the ghost propagator, which, in the gluon case, is supplemented with a pair of complex conjugate poles. Possible implications of the existence of these poles are briefly addressed.

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“…It turns out that the violation of reflection positivity is an immediate consequence of the facts that the gluon propagator has a pair of com-plex conjugate poles and that the spectral function of the gluon propagator has negative value on the whole range, see [21]. See e.g., [22,23] for the construction of the spectral function from the Euclidean data of numerical simulations on the lattice.…”

Section: Arxiv:190208894v3 [Hep-th] 6 Feb 2020mentioning

confidence: 99%

Reflection positivity and complex analysis of the Yang–Mills theory from a viewpoint of gluon confinement

et al. 2020

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In order to understand the confining decoupling solution of the Yang-Mills theory in the Landau gauge, we consider the massive Yang-Mills model which is defined by just adding a gluon mass term to the Yang-Mills theory with the Lorentz-covariant gauge fixing term and the associated Faddeev-Popov ghost term. First of all, we show that massive Yang-Mills model is obtained as a gauge-fixed version of the gauge-invariantly extended theory which is identified with the gauge-scalar model with a single fixed-modulus scalar field in the fundamental representation of the gauge group. This equivalence is obtained through the gauge-independent description of the Brout-Englert-Higgs mechanism proposed recently by one of the authors. Then, we reconfirm that the Euclidean gluon and ghost propagators in the Landau gauge obtained by numerical simulations on the lattice are reproduced with good accuracy from the massive Yang-Mills model by taking into account one-loop quantum corrections. Moreover, we demonstrate in a numerical way that the Schwinger function calculated from the gluon propagator in the Euclidean region exhibits violation of the reflection positivity at the physical point of the parameters. In addition, we perform the analytic continuation of the gluon propagator from the Euclidean region to the complex momentum plane towards the Minkowski region. We give an analytical proof that the reflection positivity is violated for any choice of the parameters in the massive Yang-Mills model, due to the existence of a pair of complex conjugate poles and the negativity of the spectral function for the gluon propagator to one-loop order. The complex structure of the propagator enables us to explain why the gluon propagator in the Euclidean region is well described by the Gribov-Stingl form. We try to understand these results in light of the Fradkin-Shenker continuity between confinement-like and Higgs-like regions in a single confinement phase in the complementary gauge-scalar model.

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Spectral representation of lattice gluon and ghost propagators at zero temperature

Cited by 53 publications

References 58 publications

Some remarks on the spectral functions of the Abelian Higgs model

Some remarks on the spectral functions of the Abelian Higgs model

Spectral functions of confined particles

Reflection positivity and complex analysis of the Yang–Mills theory from a viewpoint of gluon confinement

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