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Quantum field theory arises from the requirement that the S-matrix is lorentz scalar and obeys the cluster decomposition principle.

I want to know if there are other ways to build invariant S-Matrices that obey the cluster decomposition principle without using quantum field theory. QFT is the most natural way to do it but I'm interested in other possible approaches.

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  • $\begingroup$ It would seem like string theory should also have a consistent S-matrix, though it is not a theory of particles (hence not exactly a QFT) $\endgroup$ – Siva May 16 '13 at 22:28
  • $\begingroup$ Try browsing the string theory questions on physics.SE. The S-matrix for strings has been talked about quite a bit though I can't pull up the relevant questions right away. $\endgroup$ – Siva May 16 '13 at 23:28

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