Orlando Oliveira

University of Coimbra | UC · Department of Physics

A minimal truncated set of the integral Dyson–Schwinger equations, in Minkowski spacetime, that allows to explore QED beyond its perturbative solution is derived for general linear covariant gauges. The minimal set includes the equations for the fermion and photon propagators, the photon-fermion vertex, and the two-photon-two-fermion one-particle-i...

The temperature dependence of the Landau gauge ghost propagator is investigated in pure SU(3) Yang-Mills theory with lattice QCD simulations. Its behavior around the confined-deconfined phase transition temperature, $T_c \sim 270$ MeV, is investigated. The simulations show that in the deconfined phase, the ghost propagator is enhanced for small mom...

We study the gauge dependence of the quark propagator in quantum chromodynamics by solving the gap equation with a nonperturbative quark-gluon vertex which is constrained by longitudinal and transverse Slavnov-Taylor identities, the discrete charge conjugation and parity symmetries and which is free of kinematic singularities in the limit of equal...

The quark-gluon vertex is an important object of QCD. Studies have shown that this quantity is relevant for the dynamical chiral symmetry breaking pattern in the vacuum. The goal of our project is to obtain the quark-gluon vertex at finite temperature around the deconfinement/chiral transition using the tools provided by lattice QCD. It will be the...

The ghost propagator in Landau gauge is studied at finite temperature below and above $T_c$ using lattice QCD simulations. For high temperatures, we find that the ghost propagator is enhanced, compared to the confined phase. The results suggest that the ghost propagator can be used to identify the phase transition, similarly to the gluon propagator...

The lattice Landau gauge photon propagator for the pure gauge theory is revisited by using large lattices. For the confined case we show that it has an associated linearly growing potential, it has a mass gap, that is related to the presence of monopoles, and its spectral function violates positivity. In the deconfined phase, our simulations sugges...

The ghost propagator in Landau gauge is studied at finite temperature below and above T c using lattice QCD simulations. For high temperatures, we find that the ghost propagator is enhanced, compared to the confined phase. The results suggest that the ghost propagator can be used to identify the phase transition, similarly to the gluon propagator c...

The analytic structure of the two flavorful QCD lattice Landau gauge quark propagator is investigated with Padé approximants applied to its vector and scalar form factors. No poles at complex momentum are observed for the propagator. Moreover, there is clear evidence of a pole at real on-axis negative Euclidean momentum, i.e., for a Minkowski type...

The lattice Landau gauge photon propagator for the pure gauge theory is revisited using large lattices. For the confined case we show that it has an associated linearly growing potential, it has a mass gap, that is related to the presence of monopoles, and its spectral function violates positivity. In the deconfined phase, our simulations suggest t...

The analytic structure of the 2 flavour full QCD lattice Landau gauge quark propagator is investigated with Pad\'e approximants applied to its vector and scalar form factors. No poles at complex momentum are observed for the propagator. Moreover, there is clear evidence of a pole at real on-axis negative Euclidean momentum, i.e. for Minkowski type...

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 β. Herein, the connection between confinement and positivity violation through the Schwinger function associated...

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...

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. Herein, the connection between confinement and positivity violation through the Schwinger function associated with the Lan...

The estimation of the Källén–Lehmann spectral density from gauge invariant lattice QCD two point correlation functions is proposed, and explored via an appropriate inversion method. As proof of concept the SU(2) glueball spectrum for the quantum numbers JPC=0++ is investigated for various values of the lattice spacing. The spectral density and the...

We study the gauge dependence of the quark propagator in QCD by solving the gap equation with a nonperturbative quark-gluon vertex derived from Slavnov-Taylor identities and gauge covariance. To this end, we employ gluon propagators in renormalizable $R_\xi$ gauges from lattice-QCD. We observe a net linear increase proportional to the gauge-fixing...

We revisit the computation of the three-gluon vertex in the Landau gauge using lattice QCD simulations with large physical volumes of ~ (6.5 fm) ⁴ and ~ (8 fm) ⁴ and large statistical ensembles. For the kinematical configuration analysed, that is described by a unique form factor, an evaluation of the lattice artefacts is also performed. Particular...

In this work we investigate the lattice Landau gauge photon propagator together with the average number of Dirac strings in the compact formulation of QED for the pure gauge version of the theory as a function of the coupling constant. Their β dependence show that these two quantities can be used to identify the confinement-deconfinement transition...

The estimation of the K\"all\'en-Lehmann spectral density from gauge invariant lattice QCD two point correlation functions is proposed, and explored via an inversion strategy based on Tikhonov regularisation. We test the method on a mesonic toy model, showing that our methodology is competitive with the traditional Maximum Entropy Method. As proof...

Lattice tensor representations are used to investigate the lattice Landau gauge gluon propagator for the 4-dimensional pure SU(3) Yang-Mills gauge theory. Due to the different symmetry structure of hypercubic lattices compared to the continuum space-time, lattice correlation functions are described by different tensor structures. Therefore, form fa...

We study the Landau-gauge quark-gluon vertex with 2 flavours of O(a)improved Wilson fermions, for several lattice spacings and quark masses. In the limit of vanishing gluon momentum, we find that all nonzero form factors have a significant infrared strength, and that the leading form factor lambda_1, multiplying the tree-level vertex structure, is...

We revisit the computation of the three-gluon vertex in the Landau gauge using lattice QCD simulations with large physical volumes of $\sim$ (6.5 fm)$^ 4$ and $\sim$ (8 fm)$^ 4$ and large statistical ensembles. For the kinematical configuration analysed, that is described by a unique form factor, an evaluation of the lattice artefacts is also perfo...

It has long been known that there is a phase transition between confined and unconfined phases of compact pure gauge QED on the lattice. In this work we report three manifestations of this phase change as seen in the Landau gauge photon propagator, the static potential, and distribution of Dirac Strings in the gauge fixed configurations. Each of th...

The lattice three-gluon vertex in the Landau gauge is revisited using a large physical volume $\sim(8\textrm{fm})^4$ and a large statistical ensemble. The improved calculation explores the symmetries of the hypercubic lattice to reduce the statistical uncertainties and addresses the evaluation of the lattice artefacts. Special attention is given to...

We report on a study of the analytical structure of the Landau gauge gluon, ghost and quark propagators taken from lattice simulations using large physical volumes, to better access the IR region, and large gauge ensembles to reduce the statistical uncertainties. The investigation uses Pad\'e approximants to look at poles and branch cuts for each o...

In this work we investigate the lattice Landau gauge photon propagator together with the average number of Dirac strings in the compact formulation of QED for the pure gauge version of the theory as a function of the coupling constant. Their $\beta$ dependence show that these two quantities can be used to identify the confinement-deconfinement tran...

In BRST-quantised Yang-Mills theory the existence of BRST symmetry imposes significant constraints on the analytic structure of the continuum theory. In particular, the presence of this symmetry in the non-perturbative regime implies that any on-shell state with vanishing norm must have an associated partner state with identical mass, but negative...

In BRST-quantised Yang-Mills theory the existence of BRST symmetry imposes significant constraints on the analytic structure of the continuum theory. In particular, the presence of this symmetry in the non-perturbative regime implies that any on-shell state with vanishing norm must have an associated partner state with identical mass, but negative...

We study the quark-gluon vertex in the limit of vanishing gluon momentum using lattice QCD with two flavors of O(a) improved Wilson fermions, for several lattice spacings and quark masses. We find that all three form factors in this kinematics have a significant infrared strength and that both the leading form factor λ1, multiplying the tree-level...

In this work we report on the Landau gauge photon propagator computed for pure gauge 4D compact QED in the confined and deconfined phases and for large lattice volumes: 324, 484 and 964. In the confined phase, compact QED develops mass scales that render the propagator finite at all momentum scales and no volume dependence is observed for the simul...

Lattice tensor representations are explored to investigate the lattice Landau gauge gluon propagator for the pure SU(3) Yang-Mills gauge theory in four dimensions. The analysis of several tensor bases allows to quantify the completeness of the tensor bases considered and the deviations of the lattice results from the continuum theory, and to estima...

The estimation of the K\"all\'en-Lehmann spectral density from gauge invariant lattice QCD two point correlation functions is proposed, and explored via an appropriate inversion method. As proof of concept the SU(2) glueball spectrum for the quantum numbers $J^{PC} = 0^{++}$ is investigated for various values of the lattice spacing. The spectral de...

We study the quark-gluon vertex in the limit of vanishing gluon momentum using lattice QCD with 2 flavors of O(a) improved Wilson fermions, for several lattice spacings and quark masses. We find that all three form factors in this kinematics have a significant infrared strength, and that both the leading form factor $\lambda_1$, multiplying the tre...

In this work we report on the Landau gauge photon propagator computed for 4D compact QED in the confined and deconfined phases and for large lattices volumes: $32^4$, $48^4$ and $96^4$. In the confined phase, compact QED develops mass scales that render the propagator finite at all momentum scales and no volume dependence is observed for the simula...

The use of lattice tensor representations is explored to investigate the lattice Landau gauge gluon propagator for the pure SU(3) Yang-Mills gauge theory in 4D. The analysis of several tensor bases allows to quantify the completeness of the various tensor bases considered, the deviations of the lattice results from the continuum theory due to the l...

Starting from the lattice Landau gauge gluon and ghost propagator data we use a sequence of Padé approximants, identify the poles and zeros for each approximant and map them into the analytic structure of the propagators. For the Landau gauge gluon propagator the Padé analysis identifies a pair of complex conjugate poles and a branch cut along the...

Starting from the lattice Landau gauge gluon and ghost propagator data we use a sequence of Pad\'e approximants, identify the poles and zeros for each approximant and map them into the analytic structure of the propagators. For the Landau gauge gluon propagator the Pad\'e analysis identifies a pair of complex conjugate poles and a branch cut along...

The Schwinger-Dyson quark equation (SDE) combined with results from lattice simulation for the propagators are used to obtain information on the quark-gluon vertex, taking into account the recent full QCD lattice results for the soft-gluon limit. Its inclusion leads to a clear enhancement of the infrared quark-gluon vertex. We also find that the re...

The Schwinger–Dyson quark equation (SDE) combined with results from lattice simulation for the propagators are used to obtain information on the quark-gluon vertex, taking into account the recent full QCD lattice results for the soft-gluon limit. Its inclusion leads to a clear enhancement of the infrared quark-gluon vertex. We also find that the re...

We consider the analytic continuation of Euclidean propagator data obtained from 4D simulations to Minkowski space. In order to perform this continuation, the common approach is to first extract the Källén-Lehmann spectral density of the field. Once this is known, it can be extended to Minkowski space to yield the Minkowski propagator. However, obt...

Gauge theory correlators are potentially more singular in the infrared than those in non-gauge theories. We determine the implications that these singularities have on the spectrum of the theory, proving that the appearance of generalised poles implies the existence of on-shell states with fixed mass, but zero norm. For quantum chromodynamics these...

We report on the lattice computation of the quark propagator at finite temperature in the Landau gauge, using quenched gauge configurations. The propagator form factors are computed for various temperatures, above and below the gluon deconfinement temperature $T_c$, and for all the Matsubara frequencies. Our results suggest a strong connection betw...

Oscillons are time-dependent, localized in space, extremely long-lived states in nonlinear scalar-field models, while kinks are topological solitons in one spatial dimension. In the present work, we show new classes of oscillons and oscillating kinks in a system of two nonlinearly coupled scalar fields in 1+1 spatiotemporal dimensions. The solution...

The quark propagator at finite temperature is investigated using quenched gauge configurations. The propagator form factors are investigated for temperatures above and below the gluon deconfinement temperature Tc and for the various Matsubara frequencies. Significant differences between the functional behaviour below and above Tc are observed both...

Gauge theory correlators are potentially more singular in the infrared than those in non-gauge theories. We determine the implications that these singularities have on the spectrum of the theory, proving that the appearance of generalised poles implies the existence of on-shell states with fixed mass, but zero norm. For quantum chromodynamics these...

Oscillons are time-dependent, localized in space, extremely long-lived states in nonlinear scalar-field models, while kinks are topological solitons in one spatial dimension. In the present work, we show new classes of oscillons and oscillating kinks in a system of two nonlinearly coupled scalar fields in $1 + 1$ spatiotemporal dimensions. The solu...

We compute the Landau gauge quark propagator from lattice QCD with two flavors of dynamical O(a)-improved Wilson fermions. The calculation is carried out with lattice spacings ranging from 0.06 fm to 0.08 fm, with quark masses corresponding to pion masses mπ≈420, 290 and 150 MeV, and for volumes of up to (4.5 fm)4. Our ensembles allow us to evaluat...

The quark propagator at finite temperature is investigated using quenched gauge configurations. The propagator form factors are investigated for temperatures above and below the gluon deconfinement temperature $T_c$ and for the various Matsubara frequencies. Significant differences between the functional behaviour below and above $T_c$ are observed...

The Dyson–Schwinger quark equation is solved for the quark-gluon vertex using the most recent lattice data available in the Landau gauge for the quark, gluon and ghost propagators, the full set of longitudinal tensor structures in the Ball-Chiu vertex, taking into account a recently derived normalisation for a quark-ghost kernel form factors and th...

We consider the analytic continuation of Euclidean propagator data obtained from 4D simulations to Minkowski space. In order to perform this continuation, the common approach is to first extract the K\"all\'en-Lehmann spectral density of the field. Once this is known, it can be extended to Minkowski space to yield the Minkowski propagator. However,...

We discuss possible definitions of the Faddeev-Popov matrix for the minimal linear covariant gauge on the lattice and present preliminary results for the ghost propagator.

We study the Landau gauge quark propagator, at finite temperature, using quenched lattice simulations. Special focus is given to the behaviour of the momentum space form factors across the confinement-deconfinement phase transition.

We discuss a possible definition of the Faddeev-Popov matrix for the minimal linear covariant gauge on the lattice and present first results for the ghost propagator. We consider Yang-Mills theory in four space-time dimensions, for SU(2) and SU(3) gauge groups.

We discuss the subtleties concerning the lattice computation of the ghost propagator in linear covariant gauges, and present preliminary numerical results.

We report on results for the Landau gauge gluon propagator computed from large statistical ensembles and look at the compatibility of the results with the Gribov-Zwanziger tree level prediction for its refined and very refined versions. Our results show that the data is well described by the tree level estimate only up to momenta $p \lesssim 1$ GeV...

We discuss a possible definition of the Faddeev-Popov matrix for the minimal linear covariant gauge on the lattice and present first results for the ghost propagator. We consider Yang-Mills theory in four space-time dimensions, for SU(2) and SU(3) gauge groups.

We compute the Landau gauge quark propagator from lattice QCD with two flavors of dynamical O(a)-improved Wilson fermions. The calculation is carried out with lattice spacings ranging from 0.06 fm to 0.08 fm, with quark masses corresponding to pion masses of 420, 290 and 150 MeV, and for volumes of up to (4.5fm)^4. Our ensembles allow us to evaluat...

An approximate dual representation for non-Abelian lattice gauge theories in terms of a new set of dynamical variables, the plaquette occupation numbers (PONs) that are natural numbers, is discussed. They are the expansion indices of the local series of the expansion of the Boltzmann factors for every plaquette of the Yang–Mills action. After study...

We solve the Dyson-Schwinger quark equation for the quark-gluon vertex taking for the quark, gluon and ghost propagators the most recent lattice data available in the Landau gauge. In our approach we go beyond the Ball-Chiu type of vertex by including other tensor structures that results on a vertex that is a function of the incoming quark momentum...

The soft gluon limit of the longitudinal part of the quark-gluon vertex is studied by resorting to non-perturbative approaches to Quantum Chromodynamics (QCD). Based on a Slavnov-Taylor identity (STI), the longitudinal form factors is expressed in terms of the quark-ghost kernel, the quark self energy and the quark wave function. An exact relation...

The soft gluon limit of the longitudinal part of the quark-gluon vertex is studied by resorting to non-perturbative approaches to quantum chromodynamics (QCD). Based on a Slavnov–Taylor identity (STI), the longitudinal form factors is expressed in terms of the quark-ghost kernel, the quark self energy and the quark wave function. An exact relation...

In this work, we report on the possibility of occurrence of oscillon configurations in the fourth state of matter. Oscillons are extremely long-lived, time-periodic, spatially-localised scalar field structures. Starting from a scalar field theory in 1+1 space-time dimensions, we find out that small-amplitude oscillons can be obtained in the framewo...

The compatibility of the results from the Gribov-Zwanziger tree level prediction and lattice simulations, using large statistical ensembles, for the Landau gauge gluon propagator are investigated, thereby complementing earlier work using small-scale statistics. Our results show that the data is well described by the tree level estimate only up to m...

We report on the lattice computation of the Landau gauge gluon propagator at finite temperature, including the non-zero Matsubara frequencies. Moreover, the corresponding K\"all\'en-Lehmann spectral density is computed, using a Tikhonov regularisation together with the Morozov discrepancy principle. Implications for gluon confinement are also discu...

The lattice Landau gauge gluon propagator at finite temperature is computed including the non-zero Matsubara frequencies. Furthermore, the K\"all\'en-Lehmann representation is inverted and the corresponding spectral density evaluated using a Tikhonov regularisation together with the Morozov discrepancy principle. Implications for gluon confinement...

The quenched gluon and ghost propagator data published in [1] is reanalysed following the suggestion of [2] to resolve the differences between the infrared data of the simulations. Our results confirms that the procedure works well either for the gluon or for the ghost propagator but not for both propagators simultaneously as the observed deviation...

The gluon propagator is investigated at finite temperature via lattice simulations. In particular, we discuss its interpretation as a massive-type bosonic propagator. Moreover, we compute the corresponding spectral density and study the violation of spectral positivity. Finally, we explore the dependence of the gluon propagator on the phase of the...

A dual representation for non-Abelian lattice gauge theories where the new set of dynamical variables belong to the natural numbers $\mathbb{N}_{0}$ is discussed. After looking at the constraints on the dual variables due to gauge symmetry, the theory for the gauge group SU(2) is solved using Monte Carlo simulations based on Prokof'ev-Svistunov wor...

The two point gluon and ghost correlation functions and the three gluon vertex are investigated, in the Landau gauge, using lattice simulations. For the two point functions, we discuss the approach to the continuum limit looking at the dependence on the lattice spacing and volume. The analytical structure of the propagators is also investigated by...