  In this work we apply Thompson's method (of the dimensions and scales) to
study some features of the Quantum Electro and Chromodynamics. This heuristic
method can be considered as a simple and alternative way to the Renormalisation
Group (R.G.) approach and when applied to QED-lagrangian is able to obtain in a
first approximation both the running coupling constant behavior of alpha(mu)
and the mass m(mu).The calculations are evaluated just at d_c=4, where d_c is
the upper critical dimension of the problem, so that we obtain the logarithmic
behavior both for the coupling alpha and the excess of mass Delta m on the
energy scale mu. Although our results are well-known in the vast literature of
field theories,it seems that one of the advantages of Thompson's method, beyond
its simplicity is that it is able to extract directly from QED-lagrangian the
physical (finite) behavior of alpha(mu) and m(mu), bypassing hard problems of
divergences which normally appear in the conventional renormalisation schemes
applied to field theories like QED. Quantum Chromodynamics (QCD) is also
treated by the present method in order to obtain the quark condensate value.
Besides this, the method is also able to evaluate the vacuum pressure at the
boundary of the nucleon. This is done by assumming a step function behavior for
the running coupling constant of the QCD, which fits nicely to some quantities
related to the strong interaction evaluated through the MIT-bag model.
