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arXiv · 2203.00676

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

Lee C. Loveridge·Orlando Oliveira·Paulo J. Silva
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Abstract

The lattice regularized pure gauge compact U(1) theory is an ideal laboratory to explore how confinement is realized as its phase diagram has a confined and a deconfined phase that depends on the value of the coupling constant, i.e. on $\beta$. Herein, the connection between confinement and positivity violation through the Schwinger function associated with the Landau gauge photon propagator is investigated. The simulations reported show a very clear link between the realization of confinement and positivity violation of the photon Schwinger function and, therefore, of the photon K\"all\'en-Lehmann spectral density. Furthermore, a mass scale that characterizes the decay of the Schwinger function for small time separations is computed and used to distinguish the two phases of the theory.

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Lee C. Loveridge, Orlando Oliveira, Paulo J. Silva. 2022-03-01. The Schwinger function, confinement and positivity violation in pure gauge QED. https://doi.org/10.1103/physrevd.106.l011502

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