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Few-Body Systems

, 60:49 | Cite as

Quark Propagator in Minkowski Space

  • E. L. Solis
  • C. S. R. Costa
  • V. V. Luiz
  • G. KreinEmail author
Article
  • 60 Downloads
Part of the following topical collections:
  1. Ludwig Faddeev Memorial Issue

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.

Notes

Acknowledgements

Work partially supported by: Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES, Grant No. 8888.330776 (C.S.R.C.), 8888.330775 (E.L.S.), 8888.330773 (V.V.L.), Conselho Nacional de Desenvolvimento Científico e Tecnológico - CNPq, Grant No. 305894/2009-9 (G.K.), 464898/2014-5(G.K) (INCT Física Nuclear e Aplicações), Fundação de Amparo à Pesquisa do Estado de São Paulo - FAPESP, Grant No. 2013/01907-0 (G.K.).

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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Instituto de Física TeóricaUniversidade Estadual PaulistaSão PauloBrazil

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