The inability, in the 1950s and 1960s, of traditional quantum field theory to provide a basis for reliable calculations in strong-interaction physics led to quite diverse theoretical responses, just as had the previous divergence problems for QFT in the 1930s. We have already discussed dispersion relations and the mass-shell field theory programs. Another attempt has been the axiomatic field theory approach begun by Arthur Wightman at Princeton. Freeman Dyson has recently even made the claim:

Wightman (1989) has written an historical outline of this program and a thorough discussion of it would require an entire, highly technical case study of its own. That particular axiomatic approach has not had a strong impact on high-energy theory and we shall not discuss it further. We mention it just as an example of one reaction to the impasse encountered by standard Lagrangian quantum field theory. Our story is of another reaction, the S-matrix program. In this chapter we examine the autonomous S-matrix program some envisaged once Chew had made a radical break with quantum field theory.

Landau had argued that the only directly observable variables were those associated with essentially asymptotically free particles (before or after a scattering process), such as their initial or final momenta.