SUMMING LOGARITHMS IN QUANTUM-FIELD THEORY - THE RENORMALIZATION-GROUP

The process of renormalization in quantum field theory necessarily inv olves the introduction of an arbitrary mass scale mu(2) into the theor y. The effect of having this parameter appear due to quantum effects c an be analyzed from many points of view; the general topic is usually called the ''renormalization group.'' In this paper, one aspect of thi s feature of quantum field theory is discussed in some detail. It is s hown how the appearance of this arbitrary mass scale imposes consisten cy conditions on quantum-induced corrections to the classical action o f a model. This has the effect of determining higher order corrections in terms of lower order corrections in the perturbative expansion of the effective action, which in turn permits at least partial summation of all terms in the perturbative expansion. This is illustrated in th e context of two simple, well-understood models; a phi(4) model in fou r dimensions and a phi(3) model in six dimensions. The technicalities associated with the renormalization procedure itself are not discussed .