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

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 Källén-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.

arXiv commentVersion accepted for publication in PRD. New material added together with new extra references. It has now 8 pages and 4 Figures

References in corpus (53)

• A refinement of the Gribov-Zwanziger approach in the Landau gauge: infrared propagators in harmony with the lattice results
• Gluon and ghost propagators in the Landau gauge: Deriving lattice results from Schwinger-Dyson equations
• Lattice gluodynamics computation of Landau-gauge Green's functions in the deep infrared
• Nonabelian Superconductors: Vortices and Confinement in $\mathcal{N}=2$ SQCD
• On the infrared behavior of Landau gauge Yang-Mills theory
• Non-perturbative Propagators, Running Coupling and Dynamical Quark Mass of Landau gauge QCD
• Analytic properties of the Landau gauge gluon and quark propagators
• On the Significance of the Quantity "A Squared"
• New features of the gluon and ghost propagator in the infrared region from the Gribov-Zwanziger approach
• Indirect lattice evidence for the Refined Gribov-Zwanziger formalism and the gluon condensate $⟨A^2⟩$ in the Landau gauge
• Scaling behavior and positivity violation of the gluon propagator in full QCD
• Asymptotic Scaling and Infrared Behavior of the Gluon Propagator
• Lattice Gluon and Ghost Propagators, and the Strong Coupling in Pure SU(3) Yang-Mills Theory: Finite Lattice Spacing and Volume Effects
• Positivity violation for the lattice Landau gluon propagator
• Spectral functions of confined particles
• Reconstructing the gluon
• Källén-Lehmann spectroscopy for (un)physical degrees of freedom
• Gluon propagator and three-gluon vertex with dynamical quarks
• Infrared Gluon and Ghost Propagators
• The gluon propagator close to criticality
• Reconstructing QCD Spectral Functions with Gaussian Processes
• Massless Mode and Positivity Violation in Hot QCD
• A numerical study of confinement in compact QED
• Abelian Magnetic Monopole Dominance in Quark Confinement
• Ghost spectral function from the spectral Dyson-Schwinger equation
• Compact QED under scrutiny: it's first order
• Spectral representation of lattice gluon and ghost propagators at zero temperature
• Gluon-propagator functional form in the Landau gauge in SU(3) lattice QCD: Yukawa-type gluon propagator and anomalous gluon spectral function
• Positivity violations in QCD
• The low-momentum ghost dressing function and the gluon mass
• The generalised infrared structure of the gluon propagator
• The analytic structure of the lattice Landau gauge gluon and ghost propagators
• Double-winding Wilson loops and monopole confinement mechanisms
• The gluon propagator in linear covariant $R_{\xi }$ gauges
• Four-dimensional pure compact U(1) gauge theory on a spherical lattice
• SU(2) lattice gluon propagators at finite temperatures in the deep infrared region and Gribov copy effects
• Three-quark potential and Abelian dominance of confinement in SU(3) QCD
• Monopole condensation and colour confinement
• Reconstructing confined particles with complex singularities
• Fermionic spectral functions with the Functional Renormalization Group
• SU(3) Landau gauge gluon and ghost propagators using the logarithmic lattice gluon field definition
• Gribov copies, avalanches and dynamic generation of a gluon mass
• 4d ensembles of percolating center vortices and monopole defects: the emergence of flux tubes with N-ality and gluon confinement
• Symmetry restoration and the gluon mass in the Landau gauge
• Topological confinement of vortices in two-flavor dense QCD
• Chiral non-Abelian vortices and their confinement in three flavor dense QCD
• Lattice Gauge Fixing and the Violation of Spectral Positivity
• Lattice pure gauge compact QED in the Landau gauge: the photon propagator, the phase structure and the presence of Dirac strings
• Kugo-Ojima confinement and QCD Green's functions in covariant gauges
• The lattice Landau gauge photon propagator for 4D compact QED
• Lattice Gauge Fixing as Quenching and the Violation of Spectral Positivity
• Panel discussion: What {\it don't} we know about confinement?
• Non-perturbative BRST symmetry and the spectral structure of the ghost propagator

Cited by in corpus (4)

• Neural network approach to reconstructing spectral functions and complex poles of confined particles
• Analytic continuation and physical content of the gluon propagator
• Looking at QED with Dyson-Schwinger equations: basic equations, Ward-Takahashi identities and the two-photon-two-fermion irreducible vertex
• Compact QED: the photon propagator, confinement and positivity violation for the pure gauge theory