Hadronic Observables from Dyson–Schwinger and Bethe–Salpeter equations

Hèlios Sanchis-Alepuz,Richard Williams

doi:10.1088/1742-6596/631/1/012064

Hèlios Sanchis-Alepuz, Richard Williams

Open Access

https://doi.org/10.1088/1742-6596/631/1/012064

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Abstract

In these proceedings we present a mini-review on the topic of the Dyson–Schwinger/Bethe–Salpeter approach to the study of relativistic bound-states in physics. In particular, we present a self-contained discussion of their derivation, as well as their truncation such that important symmetries are maintained.

Highlights

In Quantum Chromodynamics (QCD) the only observable objects are hadrons, which appear as bound-states of the elementary quark and gluon degrees of freedom
Most phenomenological aspects of QCD are essentially non-perturbative problems and require an appropriate framework for their study. One such approach is the combination of Dyson–Schwinger (DSE) and Bethe-Salpeter (BSE) equations that provide a means to study the non-perturbative properties of hadrons – at the microscopic level – without abandoning a priori the principles of QCD as a scale dependent continuum quantum field theory
We devote these proceedings to a concise exposition of known results about how this framework can be systematically constructed as well as a description of the main technical issues faced upon solving the Dyson–Schwinger equations (DSEs) and BSEs in combination

Summary

Introduction

In Quantum Chromodynamics (QCD) the only observable objects are hadrons, which appear as bound-states of the elementary (but not observed) quark and gluon degrees of freedom. One such approach is the combination of Dyson–Schwinger (DSE) and Bethe-Salpeter (BSE) equations that provide a means to study the non-perturbative properties of hadrons – at the microscopic level – without abandoning a priori the principles of QCD as a scale dependent continuum quantum field theory We devote these proceedings to a concise exposition of known results about how this framework can be systematically constructed as well as a description of the main technical issues faced upon solving the DSEs and BSEs in combination. Upon a vertex expansion we generate the infinite tower of non-linear integral equations that relate the fundamental Green’s functions of the quantum field theory to one-another.

Bilocal case

Tri-local

Conclusions