  We extend the previously introduced constructive modular method to
nonperturbative QFT. In particular the relevance of the concept of ``quantum
localization'' (via intersection of algebras) versus classical locality (via
support properties of test functions) is explained in detail, the wedge
algebras are constructed rigorously and the formal aspects of double cone
algebras for d=1+1 factorizing theories are determined. The well-known on-shell
crossing symmetry of the S-Matrix and of formfactors (cyclicity relation) in
such theories is intimately related to the KMS properties of new quantum-local
PFG (one-particle polarization-free generators) of these wedge algebras. These
generators are ``on-shell'' and their Fourier transforms turn out to fulfill
the Zamolodchikov-Faddeev algebra. As the wedge algebras contain the crossing
symmetry informations, the double cone algebras reveal the particle content of
fields. Modular theory associates with this double cone algebra two very useful
chiral conformal quantum field theories which are the algebraic versions of the
light ray algebras.
