One of the main problems of modern theories in physics is the complex mathematical apparatus used for the explanation of relevant laws. Increasingly it is necessary the development of new mathematical methods to make more comprehensible laws that describe the phenomena in the atomic and nuclear world. A particular case of this problem is the Dirac theory. This paper presents a new method for applying the theory of distributions to the Dirac theory, which is characterized by its simplicity in the mathematical expressions. Here the Fourier transform has a fundamental role. This method, in principle, can be applied to the study of any issue in which distributions are used. As an example the principle of correspondence for free relativistic particles is examined.