Chiral symmetry breaking and the effective action in Abelian chromodynamics

Abelian chromodynamics is investigated using the singular infrared asymptotic behavior $(k^2)^{-2}$ of the gluon propagator. The method of functional integration is used to introduce bilocal variables that describe the meson fields. It is shown that in the model there is dynamical breaking of the chiral symmetry, the pions playing the part of the Goldstone bosons. Expressions are obtained for the dependence of the quark constituent mass and the magnitude of the quark condensate on the momentum cutoff that determines the meson form factor. Calculations are made of the meson mass spectrum and the total effective action that describes the interaction of the scalar and pseudoscalar mesons. For cutoff momentum $\Lambda=1$ GeV and quark current mass $m_0=5$ MeV the calculated pion mass is $m_\pi=140$ MeV, the dynamical quark mass is $m=241$ MeV, and the quark condensate is $\langle\overline uu\rangle=\langle\overline dd\rangle=-(248\;\text{MeV})^3$.