Abstract:

We present a method of analytic regularization with which any element of the S-matrix becomes an analytic function of a complex parameter. The usual divergences appear simply as poles at the physical value of the parameter. The subtraction of these poles leads to the usual finite parts. A simple example is discussed, in which the mathematical justification for these subtractions is given. In the consideration of this example we discuss the causal Green functions of the iterated D'Alembertian. They are constructed from the retarded and advanced solutions introduced by M. Riesz. The application to the self-energy of the electron is explicitly given. An heuristic deduction is then used to convert the problem of the evaluation of the self-energy into the problem of solving a differential equation. The self-energy integral is a formal solution of the latter equation, the finite part (with the pole subtracted) being a rigorous solution. © 1964 Società Italiana di Fisica.