  The concept of effective particles as degrees of freedom in a relativistic
quantum field theory is defined using a non-perturbative renormalization group
procedure for Hamiltonians. However, every candidate for a basic physical
theory appears to require an initial perturbative search for the set of
interaction terms that may provide a basis with which the full effective theory
Hamiltonian could be constructed in a series of successive approximations. This
article describes the required perturbative expansion and illustrates it with a
set of general 4th-order formulae.
