# Accession Number:

## AD0281803

# Title:

## SELF-COUPLED MESON FIELD. EQUATIONS FOR SINGLE PROPAGATORS, THEIR SOLUTION FOR A NUMERICAL MODEL, CONSIDERATIONS ON THE CONVERGENCE OF PERTURBATIVE EXPANSIONS,

# Descriptive Note:

# Corporate Author:

## NAPLES UNIV (ITALY)

# Personal Author(s):

# Report Date:

## 1962-07-01

# Pagination or Media Count:

## 16.0

# Abstract:

It is shown that all the independent equations, or conditions, that can be derived for a single propagation kernel from all the branching equations that connect it and its derivatives with respect to the parameters of the theory with kernels of arbitrarily high order redice to a small and unique set. It is then shown that whereas the only information one can get from the majoration of a regularized perturbative expansion of the kernels is that all majorants are divergent, a numerical model obtained by imposing that the free propagators in configuration space depend only upon the mass can be exactly solved if these equations are used. One finds that the general solution is a linear combination of hypergeometric functions of the coupling constant 1 which is singular for 1 0 there is, however, a unique choice of constants which yields a solution regular when 1 0. This model is related to the asymptotic form of the correct theory if the latter is defined over an infinitesimal space-time volume. Author