In this work we apply Thompson's method (of the dimensions and scales) tostudy some features of the Quantum Electro and Chromodynamics. This heuristicmethod can be considered as a simple and alternative way to the RenormalisationGroup (R.G.) approach and when applied to QED-lagrangian is able to obtain in afirst 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 isthe upper critical dimension of the problem, so that we obtain the logarithmicbehavior both for the coupling alpha and the excess of mass Delta m on theenergy scale mu. Although our results are well-known in the vast literature offield theories,it seems that one of the advantages of Thompson's method, beyondits simplicity is that it is able to extract directly from QED-lagrangian thephysical (finite) behavior of alpha(mu) and m(mu), bypassing hard problems ofdivergences which normally appear in the conventional renormalisation schemesapplied to field theories like QED. Quantum Chromodynamics (QCD) is alsotreated 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 theboundary of the nucleon. This is done by assumming a step function behavior forthe running coupling constant of the QCD, which fits nicely to some quantitiesrelated to the strong interaction evaluated through the MIT-bag model.
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