Causality and dispersion relations and the role of the S-matrix in the ongoing research

摘要

The adaptation of the Kramers-Kronig dispersion relations to the causallocalization structure of QFT led to an important project in particle physics,the only one with a successful closure. The same cannot be said about thesubsequent attempts to formulate particle physics as a pure S-matrix project.The feasibility of a pure S-matrix approach are critically analyzed and theirserious shortcomings are highlighted. Whereas the conceptual/mathematicaldemands of renormalized perturbation theory are modest and misunderstandingscould easily be corrected, the correct understanding about the origin of thecrossing property requires the use of the mathematical theory of modularlocalization and its relation to the thermal KMS condition. These new concepts,which combine localization, vacuum polarization and thermal properties underthe roof of modular theory, will be explained and their potential use in a newconstructive (nonperturbative) approach to QFT will be indicated. The S-matrixstill plays a predominant role but, different from Heisenberg's andMandelstam's proposals, the new project is not a pure S-matrix approach. TheS-matrix plays a new role as a "relative modular invariant"..