Causality and dispersion relations and the role of the S-matrix in the ongoing research
Bert Schroer
January 31, 2011
The adaptation of the Kramers-Kronig dispersion relations to the causal
localization structure of QFT led to an important project in particle physics,
the only one with a successful closure. The same cannot be said about the
subsequent attempts to formulate particle physics as a pure S-matrix project.
The feasibility of a pure S-matrix approach are critically analyzed and their
serious shortcomings are highlighted. Whereas the conceptual/mathematical
demands of renormalized perturbation theory are modest and misunderstandings
could easily be corrected, the correct understanding about the origin of the
crossing property demands the use of the mathematical theory of modular
localization and its relation to the thermal KMS condition. These concepts
which combine localization, vacuum polarization and thermal properties under
the roof of modular theory will be explained and their potential use in a new
constructive (nonperturbative) approach to QFT will be indicated. The S-matrix
still plays a predominant role, but different from Heisenberg's and
Mandelstam's proposals the new project is not a pure S-matrix approach.
Keywords:
none