Confinement, quark mass functions, and spontaneous chiral symmetry breaking in Minkowski space

Understand

We formulate the covariant equations for quark-antiquark bound states in Minkowski space in the framework of the Covariant Spectator Theory.

• The quark propagators are dressed with the same kernel that describes the interaction between different quarks.
• We show that these equations are charge-conjugation invariant, and that in the chiral limit of vanishing bare quark mass, a massless pseudoscalar bound state is produced in a Nambu-Jona-Lasinio (NJL) mechanism, which is associated with the Goldstone boson of spontaneous chiral symmetry breaking.
• In this introductory paper, we test the formalism by using a simplified kernel consisting of a momentum-space delta-function with a vector Lorentz structure, to which one adds a mixed scalar and vector confining interaction.