The Schwinger function, confinement and positivity violation in pure gauge QED

Loveridge, Lee C.; Oliveira, Orlando; Silva, Paulo J.

doi:10.48550/arxiv.2203.00676

Cited by 2 publications

(2 citation statements)

References 68 publications

(78 reference statements)

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“…Another interesting topic would be to find out if the wellunderstood confinement-deconfinement transition in compact QED could be connected to a change of the associated spectral density of the photon, using the recent data of [35], perhaps in terms of having, or not, complex conjugate poles. Interesting lattice evidence linking confinement to violations of spectral positivity was presented very recently in the same model, [36].…”

Section: Discussionmentioning

confidence: 89%

Neural network approach to reconstructing spectral functions and complex poles of confined particles

Lechien¹,

Dudal²

2022

Preprint

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Reconstructing spectral functions from propagator data is difficult as solving the analytic continuation problem or applying an inverse integral transformation are ill-conditioned problems. Recent work has proposed using neural networks to solve this problem and has shown promising results, either matching or improving upon the performance of other methods. We generalize this approach by not only reconstructing spectral functions, but also (possible) pairs of complex poles or an infrared (IR) cutoff. We train our network on physically motivated toy functions, examine the reconstruction accuracy and check its robustness to noise. Encouraging results are found on both toy functions and genuine lattice QCD data for the gluon propagator, suggesting that this approach may lead to significant improvements over current state-of-the-art methods.

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Section: Discussionmentioning

confidence: 89%

Neural network approach to reconstructing spectral functions and complex poles of confined particles

Lechien¹,

Dudal²

2022

Preprint

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“…There are several features of the dynamics of a quantum field theory that cannot be explained within its perturbative solution. For example, the dynamical generation of masses, which also includes dynamical chiral symmetry breaking, can occur in QED [7][8][9][10][11][12], and certainly occurs in QCD [13,14], which together with confinement [16,17] cannot be understood within perturbation theory.…”

Section: Introductionmentioning

confidence: 99%

The Dyson-Schwinger equations and the solution of QED: exploring the two-photon-two-fermion irreducible vertex

Oliveira¹,

Lessa²,

Terin³

2022

Preprint

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A minimal truncated set of Dyson-Schwinger equations that allow exploring the non-perturbative regime of QED is derived for a general linear covariant gauge. This minimal set includes the propagators, the the photon-fermion, and the two-photon-two-fermion vertices. If the equations for the first three quantities are exact, to build a closed set of equations, the last one is truncated ignoring further higher-order Green functions. We also show that the truncated equation reproduces the lowest order perturbative result for the two-photon-two-fermion vertex in the limit of the small coupling constant. Then, the two-photon-two-fermion irreducible vertex is studied by combining the corresponding Ward-Takahashi identity with the Dyson-Schwinger equation. The longitudinal part of this irreducible vertex is computed from the Ward-Takahashi identity, which is solved in the low energy limit when one of the photons has zero energy (soft photon limit). For this kinematical configuration, the general expression for the vertex is derived and its form factors related to the photon-fermion vertex and fermion propagator. Contents I. Introduction and Motivation II. Quantum Electrodynamics -definitions and generating functionals III. The Dyson-Schwinger Equations A. The fermion gap equation B. The Dyson-Schwinger equation for the photon propagator C. A Dyson-Schwinger equation for the photon-fermion vertex IV. Ward-Takahashi Identities V. Renormalization VI. The two-photon-two-fermion one-particle irreducible vertex A. The longitudinal component of Γ µν from the Ward-Takahashi identity 1. Solving the contracted Ward-Takahashi identity 2. Low momenta solution of the Ward-Takahashi identity 3. Tensor basis for Γ µν and the solution of the Ward-Takahashi Idendity VII. The Dyson-Schwinger equation for Γ µν A. Exploring further the DSE for the two-photon-two-fermion vertex VIII.

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The Schwinger function, confinement and positivity violation in pure gauge QED

Cited by 2 publications

References 68 publications

Neural network approach to reconstructing spectral functions and complex poles of confined particles

Neural network approach to reconstructing spectral functions and complex poles of confined particles

The Dyson-Schwinger equations and the solution of QED: exploring the two-photon-two-fermion irreducible vertex

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