Quark propagator in Minkowski space

Abstract

The analytic structure of the quark propagator in Minkowski space is more complex than in Euclidean space due to the possible existence of poles and branch cuts at timelike momenta. These singularities impose enormous complications on the numerical treatment of the nonperturbative Dyson-Schwinger equation for the quark propagator. Here we discuss a computational method that avoids most of these complications. The method makes use of the spectral representation of the propagator and of its inverse. The use of spectral functions allows one to handle in exact manner poles and branch cuts in momentum integrals. We obtain model-independent integral equations for the spectral functions and perform their renormalization by employing a momentum-subtraction scheme. We discuss an algorithm for solving numerically the integral equations and present explicit calculations in a schematic model for the quark-gluon scattering kernel.

arXiv commentPrepared for the Topical Collection 'Ludwig Faddeev Memorial Issue' of Few-Body Systems

References in corpus (33)

• Baryons as relativistic three-quark bound states
• Introduction to the functional RG and applications to gauge theories
• Explanation and Prediction of Observables using Continuum Strong QCD
• QCD at finite temperature and chemical potential from Dyson-Schwinger equations
• The pion: an enigma within the Standard Model
• The Perturbative Pole Mass in QCD
• Solving Bethe-Salpeter equation in Minkowski space
• Solving Bethe-Salpeter equation for two fermions in Minkowski space
• Analytic structure of QCD propagators in Minkowski space
• Quark-gluon Vertex: A Perturbation Theory Primer and Beyond
• Advances in solving the two-fermion homogeneous Bethe-Salpeter equation in Minkowski space
• Small parameters in infrared quantum chromodynamics
• Confinement, quark mass functions, and spontaneous chiral symmetry breaking in Minkowski space
• Nonperturbative structure of the ghost-gluon kernel
• Study of relativistic bound states for scalar theories in Bethe-Salpeter and Dyson-Schwinger formalism
• The chiral condensate from renormalization group optimized perturbation
• Solving Bethe-Salpeter scattering state equation in Minkowski space
• Bethe-Salpeter bound-state structure in Minkowski space
• Minkowski solution of Dyson-Schwinger equations in momentum subtraction scheme
• Fermionic spectral functions with the Functional Renormalization Group
• Solving the Bethe-Salpeter equation for a pseudoscalar meson in Minkowski space
• Ghost Poles in the Nucleon Propagator: Vertex Corrections and Form Factors
• Dynamical chiral symmetry breaking with Minkowski space integral representations
• Exact Solutions to the Fermion Propagator Schwinger-Dyson Equation in Minkowski space with on-shell Renormalization for Quenched QED
• Implications of analyticity to solution of Schwinger-Dyson equations in Minkowski space
• Solving the three-body bound-state Bethe-Salpeter equation in Minkowski space
• Self-consistent solution of the Schwinger-Dyson equations for the nucleon and meson propagators
• Fermion spectral function in hot strongly interacting matter from the functional renormalization group
• Euclidean to Minkowski Bethe-Salpeter amplitude and observables
• Confined gluon from Minkowski space continuation of PT-BFM SDE solution
• Ghost poles in the nucleon propagator in the linear-sigma model approach and its role in pion-nucleon low-energy theorems
• Quark mass functions and pion structure in the Covariant Spectator Theory
• Quark mass functions and pion structure in Minkowski space

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