An irreducible form for the asymptotic expansion coefficients of the heat kernel of fermions in four-dimensional curved space

We consider the heat kernel for a massless fermion of spin 1/2 interacting with all types of non-Abelian boson fields, i.e. scalar, pseudo-scalar, vector, axial-vector and antisymmetric tensor fields, in a four-dimensional Riemannian space. The couplings of the fermion with the boson fields contain irreducible matrices of the product of the gamma-matrices. In this model, the components of the first and second asymptotic expansion coefficients of the heat kernel with respect to the irreducible matrices are explicitly presented. The form of the second coefficients is useful for evaluation of some fermionic anomalies in four-dimensional curved space, and the concrete forms of the chiral U(l) and the trace anomalies are presented.