We construct and solve the Dyson-Schwinger equation (DSE) of quark propagator with a parameterized metric, which connects the Euclidean metric with the Minkowskian one. We show, in some models, the Minkowskian vacuum is different from the Euclidean vacuum. The usual analytic continuation of Green function does not make sense in these cases. While with the algorithm we proposed and the quark-gluon vertex ansatz which preserves the Ward-Takahashi identity, the vacuum keeps being unchanged in the evolution of the metric. In this case, analytic continuation becomes meaningful and can be fully carried out.
We present the exact numerical solutions for the Schwinger-Dyson equations at finite temperature with general gauge in Abelian gauge theory. We then study the chiral phase transition on temperature from the obtained solutions. We find that, within the quenched Schwinger-Dyson equations, there exists substantial gauge dependence on the solutions and the critical temperature.
We study the regularization dependence on the quenched Schwinger-Dyson equations in general gauge by applying the two types of regularizations, the four and three dimensional momentum cutoffs. The obtained results indicate that the solutions are not drastically affected by the choice of two different cutoff prescriptions. We then think that both the regularizations can nicely be adopted in the analyses for the Schwinger-Dyson equations.
Chiral symmetry at finite temperature is studied using the Schwinger-Dyson equation. We calculate numerically the critical temperature using the Schwinger-Dyson equation with the gauge parameter that depends on an external momentum. The critical temperature obtained by this method is similar to that with the Landau gauge and wave function renormalization constant 1. Moreover, the gauge invariance in the ladder approximation is examined using our method.
We study the gauge dependence on the chiral phase transition of Quantum chromodynamics at finite temperature based on the quenched Schwinger-Dyson equation. We first solve the equations without approximations at finite temperature in general gauge, then study the gauge dependence on the critical temperature of the chiral phase transition. We find that the critical temperature drastically depends on the choice of the gauge, and the parameters at the quenched level in the Schwinger-Dyson equations.
Novel solutions of Minkowski QED2+1 and large $N_f$ QCD Schwinger-Dyson equations will be presented and discussed. The resultant propagators of confined degrees of freedom will be shown.
We investigate the properties of fermion mass functions in quantum electrodynamics calculated by the Schwinger-Dyson equation in the strong coupling region, in which the loop integration is performed in Minkowski space. The calculated results without the instantaneous exchange approximation are compared with those obtained by integration in Euclidean space.
A nonperturbative Schwinger-Dyson analysis of mass generation is presented for a non-Hermitian PT-symmetric field theory in four dimensions of an axion coupled to a Dirac fermion.The model is motivated by phenomenological considerations.The axion has a quartic self-coupling $λ$ and a Yukawa coupling $g$ to the fermion. The Schwinger-Dyson equations are derived for the model with generic couplings. In the non-Hermitian case there is an additional nonperturbative contribution to the scalar mass. In a simplified rainbow analysis the solutions for the SD equations, are given for different regimes …
We give a brief summary of the Dyson-Schwinger and Bethe-Salpeter approach to hadron spectroscopy and report on recent progress in determining resonance properties in this framework. We exemplify the extraction of resonances using a scalar model, where we solve the scattering equation for the four-point scattering amplitude and extract the pole locations on the second Riemann sheet as well as the phase shifts.
The solution to the Schwinger-Dyson equation that describes the summation over Pomeron loop diagrams is derived. The solution is a closed expression which splits into two parts. The first leads directly to the renormalization of the BFKL Pomeron, and the second contribution is equivalent to non interacting Pomerons with renormalized vertices. Thus a closed expression is derived for the sum over Pomeron loop diagrams in the perturbative QCD approach, which preserves unitarity.
The quark scalar, axial and tensor charges of nucleon are calculated in the Schwinger-Dyson formalism. We first calculate these charges in the rainbow-ladder truncation using the IR cut quark-gluon vertex, and show that the result is in agreement with the known data. We then perform the same calculation with the phenomenological IR singular quark-gluon vertex. In this case, the Schwinger-Dyson equation does not converge. We show that this result suggests the requirement of additional corrections to the rainbow-ladder truncation, due to the interaction between quark and gluons in the deep IR re…
In this contribution, we summarize a truncation-independent method to compute the equation of state within nonperturbative functional approaches. After demonstrating its viability, the method is applied to solutions obtained from a set of truncated Dyson-Schwinger equations for the quark and gluon propagators of (2+1)-flavor QCD to obtain thermodynamic quantities across the phase diagram of strong-interaction matter.
We provide a study of quantum chromodynamics with the technique of Dyson-Schwinger equations in differential form. In this way, we are able to approach the non-perturbative limit and recover, with some approximations, the 't Hooft limit of the theory. Quark mass in the propagator term goes off-shell at low-energies signaling confinement. A condition for such occurrence in the theory is provided.
We review in detail modern numerical methods used in the determination and solution of Bethe-Salpeter and Dyson--Schwinger equations. The algorithms and techniques described are applicable to both the rainbow-ladder truncation and its non-trivial extensions. We discuss pedagogically the steps involved in constructing conventional mesons and baryons as systems of two- and three-quarks respectively. As further application we describe the self-consistent calculation of form-factors and highlight the challenges that remain therein.
It is well known that some quantum and statistical fluctuations of a quantum field may be recovered by adding suitable stochastic sources to the mean field equations derived from the Schwinger-Keldysh (Closed-time-path) effective action. In this note we show that this method can be extended to higher correlations and higher (n-particle irreducible) effective actions. As an example, we investigate three and fourth order correlations by adding stochastic sources to the Schwinger - Dyson equations derived from the 2-particle irreducible effective. This method is a simple way to investigate the no…
We calculate the tensor and axial charges of the quark in the Schwinger-Dyson formalism of Landau gauge QCD. It is found that the dressed tensor and isovector axial charges of the quark are suppressed against the bare quark contribution, and the result agrees qualitatively with the experimental data. We show that this is due to the superposition of the spin flip of the quark arising from the successive emission of gluons which dress the vertex. For the isoscalar quark axial charge, we have analyzed the Schwinger-Dyson equation by including the leading unquenching quark-loop effect. It is found…
We examined the effect of an imaginary part of the ladder approximation Schwinger-Dyson equation. We show the imaginary part enhances the effect of the first order transition, and affects a tricritical point. In particular, a chemical potential at a tricritical point is moved about 200(MeV). Thus, one should not ignore the imaginary part. On the other hand, since an imaginary part is small away from a tricritical point, one should be able to ignore an imaginary part. In addition, we also examined the contribution of the wave function renormalization constant.
The Green's functions of QCD encode important information about the infrared dynamics of the theory. The main non-perturbative tools used to study them are their own equations of motion, known as Schwinger-Dyson equations, and large-volume lattice simulations. We have now reached a point where the interplay between these two methods can be most fruitful. Indeed, the quality of the lattice data is steadily improving, while a recently introduced truncation scheme for the Schwinger-Dyson equations makes their predictions far more reliable. In this talk several of the above points will be reviewed…
We summarize our results on baryon number fluctuations at nonzero temperature and chemical potential. They are obtained from solutions of a coupled set of Dyson-Schwinger equations for the quark and gluon propagators of QCD in Landau gauge with $N_f=2+1$ quark flavors. In comparison with preliminary STAR data, our results are compatible with a critical endpoint at large chemical potential and a freeze-out line that bends below it.
Using simple models in D=0+0 and D=0+1 dimensions we construct partition functions and compute two-point correlations. The exact result is compared with saddle-point approximation and solutions of Schwinger-Dyson equations. When integrals are dominated by more than one saddle-point we find Schwinger-Dyson equations do not reproduce the correct results unless the action is first transformed into dual variables.
We review the status of calculations of Yang-Mills Green functions from Dyson-Schwinger equations. The role of truncations is discussed and results for the four-gluon vertex are presented.
The variational Hamiltonian approach to Quantum Chromodynamics in Coulomb gauge is investigated within the framework of the canonical recursive Dyson--Schwinger equations. The dressing of the quark propagator arising from the variationally determined non-perturbative kernels is expanded and renormalized at one-loop order, yielding a chiral condensate compatible with the observations.
We present progress in the evaluation of $γ^* N \rightarrow N^*(1535)$ transition form factors in a quark-diquark picture of these baryons. Our analysis is based upon the fully-consistent treatment of a vector $\times$ vector contact interaction, embedded in the interlaced formalism of Schwinger-Dyson and Bethe-Salpeter equations.
We obtain the QCD quark condensate from consideration of unquenched quark dynamics in Dyson-Schwinger gluon vacuum. We consider the non-local extension of the condensate and determine the quark virtuality. We also obtain the condensate-driven contribution of the non-perturbative QCD to Euler--Heisenberg Lagrangian of QED in external electromagnetic fields.
The technicolor (TC) Schwinger-Dyson equations (SDE) should include radiative corrections induced by extended technicolor (ETC) interactions when TC is embedded into a larger theory including also QCD. These radiative corrections couple the different strongly interacting Dyson equations. We discuss how the boundary conditions of the coupled SDE system are modified by these corrections, and verify that the ultraviolet behavior of the self-energies are described by a function that decreases logarithmically with momentum.
The gluon propagator plays a central role in determining the dynamics of QCD. In this work we demonstrate for BRST quantised QCD that the Dyson-Schwinger equation imposes significant analytic constraints on the structure of this propagator. In particular, we find that these constraints control the appearance of massless components in the gluon spectral density.
Recent progress in the solution of Dyson-Schwinger equations of QCD allows for a non perturbative evaluation of the One Gluon Exchange (OGE) interaction. We calculate the interquark static potential for heavy mesons by assuming that it is given by this OGE interaction and we apply it to the description of charmonium.
An Abelian gauge theory with Chern-Simons term is investigated for a four-component Dirac fermion in 1+2 dimensions. The Ball-Chiu (BC) vertex function is employed to modify the rainbow-ladder approximation for the Schwinger-Dyson (SD) equation. We numerically solve the SD equation and show the gauge dependence for the resulting phase boundary for the parity and the chiral symmetry.
We investigate some aspects of the self-consistency in the Dyson-Schwinger approach to both the QED and the self-interacting scalar field theories. We prove that the set of the Dyson-Schwinger equations, together with the Green-Ward-Takahashi identity, is equivalent to the analogous set of integral equations studied in condensed matter, namely many-body perturbation theory, where it is solved self-consistently and iteratively. In this framework, we compute the non-perturbative solution of the gap equation for the self-interacting scalar field theory.
