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Register a new userQuasifermion spectrum at finite temperature from coupled Schwinger-Dyson equations for a fermion-boson system
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We nonperturbatively investigate a fermion spectrum at finite temperature in a chiral invariant linear sigma model. Coupled Schwinger-Dyson equations for fermion and boson are developed in the real time formalism and solved numerically. From the coupling of a massless fermion with a massive boson, the fermion spectrum shows a three-peak structure at some temperatures even for the strong coupling region. This means that the three-peak structure which was originally found in the one-loop calculation is stable against higher order corrections even in the strong coupling region.
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The dynamics of weakly coupled, non-abelian gauge fields at high temperature is non-perturbative if the characteristic momentum scale is of order |k|~ g^2 T. Such a situation is typical for the processes of electroweak baryon number violation in the early Universe. Bodeker has derived an effective theory that describes the dynamics of the soft field modes by means of a Langevin equation. This effective theory has been used for lattice calculations so far. In this work we provide a complementary, more analytic approach based on Dyson-Schwinger equations. Using methods known from stochastic quantisation, we recast Bodekers Langevin equation in the form of a field theoretic path integral. We introduce gauge ghosts in order to help control possible gauge artefacts that might appear after truncation, and which leads to a BRST symmetric formulation and to corresponding Ward identities. A second set of Ward identities, reflecting the origin of the theory in a stochastic differential equation, is also obtained. Finally Dyson-Schwinger equations are derived.
Motivated by the observation that there may exist hadronic excitations even in the quark-gluon plasma (QGP) phase, we investigate how the properties of quarks, especially within the quasi-particle picture, are affected by the coupling with bosonic excitations at finite temperature (T), employing Yukawa models with a massive scalar (pseudoscalar) and vector (axial-vector) boson of mass m. The quark spectral function and the quasi-dispersion relations are calculated at one-loop order. We find that there appears a three-peak structure in the quark spectral function with a collective nature when T is comparable with m, irrespective of the type of boson considered. Such a multi-peak structure was first found in a chiral model yielding scalar composite bosons with a decay width. We elucidate the mechanism through which the new quark collective excitations are realized in terms of the Landau damping of a quark (an antiquark) induced by scattering with the thermally excited boson, which gives rise to mixing and hence a level repulsion between a quark (antiquark) and an antiquark-hole (quark-hole) in the thermally excited antiquark (quark) distribution. Our results suggest that the quarks in the QGP phase can be described within an interesting quasi-particle picture with a multi-peak spectral function. Because the models employed here are rather generic, our findings may represent a universal phenomenon for fermions coupled to a massive bosonic excitation with a vanishing or small width. The relevance of these results to other fields of physics, such as neutrino physics, is also briefly discussed. In addition, we describe a new aspect of the plasmino excitation obtained in the hard-thermal loop approximation.
Using a technique devised by Bender, Milton and Savage, we derive the Dyson-Schwinger equations for quantum chromodynamics in differential form. We stop our analysis to the two-point functions. The t~Hooft limit of color number going to infinity is derived showing how these equations can be cast into a treatable even if approximate form. It is seen how this limit gives a sound description of the low-energy behavior of quantum chromodynamics by discussing the dynamical breaking of chiral symmetry and confinement, providing a condition for the latter. This approach exploits a background field technique in quantum field theory.
An approach based on combined solutions of the Bethe-Salpeter (BS) and Dyson-Schwinger (DS) equations within the ladder-rainbow approximation in the presence of singularities is proposed to describe the meson spectrum as quark antiquark bound states. We consistently implement into the BS equation the quark propagator functions from the DS equation, with and without pole-like singularities, and show that, by knowing the precise positions of the poles and their residues, one is able to develop reliable methods of obtaining finite interaction BS kernels and to solve the BS equation numerically. We show that, for bound states with masses $M < 1$ GeV, there are no singularities in the propagator functions when employing the infrared part of the Maris-Tandy kernel in truncated BS-DS equations. For $M >1 $ GeV, however, the propagator functions reveal pole-like structures. Consequently, for each type of mesons (unflavored, strange and charmed) we analyze the relevant intervals of $M$ where the pole-like singularities of the corresponding quark propagator influence the solution of the BS equation and develop a framework within which they can be consistently accounted for. The BS equation is solved for pseudo-scalar and vector mesons. Results are in a good agreement with experimental data. Our analysis is directly related to the future physics programme at FAIR with respect to open charm degrees of freedom.
In this talk, we review some of the current efforts to understand the phenomenon of chiral symmetry breaking and the generation of a dynamical quark mass. To do that, we will use the standard framework of the Schwinger-Dyson equations. The key ingredient in this analysis is the quark-gluon vertex, whose non-transverse part may be determined exactly from the nonlinear Slavnov-Taylor identity that it satisfies. The resulting expressions for the form factors of this vertex involve not only the quark propagator, but also the ghost dressing function and the quark-ghost kernel. Solving the coupled system of integral equations formed by the quark propagator and the four form factors of the scattering kernel, we carry out a detailed study of the impact of the quark gluon vertex on the gap equation and the quark masses generated from it, putting particular emphasis on the contributions directly related with the ghost sector of the theory, and especially the quark-ghost kernel. Particular attention is dedicated on the way that the correct renormalization group behavior of the dynamical quark mass is recovered, and in the extraction of the phenomenological parameters such as the pion decay constant.
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