Construction of Unitary, CovariantSMatrices Defined by Convergent Perturbation Series

Abstract

A method is given for the construction of $S$ matrices which are unitary and covariant. Moreover, the $S$ matrix elements are the analytic continuations to timelike momenta of quantities which are defined by convergent perturbation series for Euclidean momenta. It is shown that the $S$ matrix in the Euclidean region has the same form as the correlation functions of classical gases which interact through stable, regular pair potentials. The known results on the existence of a thermodynamic limit and convergence of activity (fugacity) series for such gases are exploited in the $S$-matrix theory. Approximation schemes suggested by the analogy are noted.