General structure of two-photon S matrix in waveguide quantum   electrodynamics systems containing a local quantum system with multiple   ground states
  We present the general structure of two-photon S matrix for a waveguide coupled to a local quantum system that supports multiple ground states. The presence of the multiple ground states results in a non-commutative aspect of the system with respect to the exchange of the orders of photons. Consequently, the two-photon S matrix significantly differs from the standard form as described by the cluster decomposition principle in the quantum field theory. 
Shanshan Xu, Shanhui Fan
quant-ph