By using the kernels consisting of the projectors and function δ(t), both the co-nvergence to equilibrium and to get the propagators in covariant gauge are solved to-gether under the vanishing initial condition. Thus, the SQ prescriptions of gauge and non-gauge fields are united in using only these same kernels. The Maxwell, Chern-Si-mon and the linear gravitational theories are considered respectively. Again, it is shown that the use of this kernel does not yield the influence on the equilibrium distri-bution.