Fermion determinant with dynamical chiral symmetry breaking

One -loop fermion determinant is discussed for the case in which dynamical chiral symmetry breaking caused by momentum dependent fermion self energy Σ(p2) take place. The obtained series generalizes the heat kernel expansion for hard fermion mass. PACS number(s): 03.65.Db, 11.10Ef, 11.30.Rd, 12.39.Fe In quantum field theory, 1-loop quantum correction of fermions is from fermion determinant. It is known how to derive an exact non-perturbative representation for the chiral fermion determinant with hard fermion mass [1] and the technique has been widely used in the literature such as to derive the effective action of quarks aiming at modeling QCD at low-energy [2–4]. The central object in the calculation of the effective action is lndet(D+m), where in the Euclidean space, the differential Dirac operator D depends on hermitian external flavor sources (or collective meson fields) which have well defined transformation laws with respect to the action of the chiral group D ≡ ∇/ − s+ ipγ5 ∇μ ≡ ∂μ − ivμ − iaμγ5 = −∇ † μ , (1) m is a hard fermion mass. Ignoring anomaly, the real part of lndet(D + m) in terms of a proper time integral is