True self energy function and reducibility in effective scalar theories. (Revized)
Published 2017-10-12Version 1
This is the revised version of Sect. I - IV of the paper https://doi.org/10.1103/PhysRevD.89.125022 originally published in 2014. The thing is that in https://doi.org/10.1103/PhysRevD.89.125022 the text was insufficiently clear and, in addition, it contained (through my fault) a few typos. This is the reason why I decided to offer a revised version. Original abstract: This is the eighth paper in the series devoted to the systematic study of effective theories. Below, I discuss the renormalization of the one-loop two-leg functions in multicomponent effective scalar theory. It is shown that only a part of numerous contributions that appear in the general expression for a two-leg graph can be considered as the true self-energy function. This part is completely fixed by the values of minimal coupling constants; it is the only one that should be taken into account in the conventional process of the summation of Dyson's chain that results in explicit expression for the full propagator. The other parts provide the well-defined finite corrections for the graphs with the number of legs n > 2. It is also shown that there is no need to attract the renormalization prescriptions for the higher derivatives of the two-leg function on the mass shell; the requirements of finiteness and diagonability turn out to be quite sufficient.