Renormalisation group, function iterations and computer algebra

The set of perturbative solutions of the renormalisation group equation relative to the coupling constant known in quantum field theory is studied. It is shown that it is generated by the continuous iteration of a particular solution. The iteration parameter, which may be complex, is the parameter of an abelian group whose generator is proportional to β. Two new lemmas are derived. They are useful to construct a simple algorithm to find the continuous iteration of various functions and to deduce trivially, from the already known iteration of a function, the continuous iteration of a whole family of functions. It is pointed out how one can find iterations of functions which do not satisfy the perturbative boundary condition. The algorithm has been implemented in REDUCE and several examples are discussed