Gauge and Lorentz Covariant Quark Propagator in an Arbitrary Gluon Field

The quark propagator in presence of an arbitrary gluon field is calculated gauge and Lorentz covariantly order by order in terms of powers of gluon field and its derivatives. The result is independent of path connecting ends of propagator and leading order result coincides with the exact propagator in the trivial case of vanishing gluon field. PACS number(s): 11.15.Tk, 12.20.Ds, 12.38.Lg, 14.65.-q The quark propagator S(x, y;A) = (i∇/ −m)(x, y) 1 with ∇ = ∂ − igA for a quark of mass m in the presence of a gluon field A plays important role in many investigations of quantum chromodynamics. Integrate out gluon field, we get physical quark propagator by −i〈0|Tψ(x)ψ(y)|0〉 = ∫ DAμ S(x, y;A)e iSQCD(A) ∫ DAμ eiSQCD(A) ≡ 〈S(x, y;A)〉 , (1) with SQCD(A) be part of QCD action for pure gluon field. Propagator S(x, y;A) is Lorentz transformation covariant and under color gauge transformation Aμ(x) → V (x)Aμ(x)V (x)− i/gV (x)[∂V (x)] transforms as S(x, y;A) → S (x, y;A) = V (x)S(x, y;A)V (y) . (2) ∗Mailing address 1Our formulae are given in Minkowski space with Bjorken Drell conventions.