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We present the general structure of two-photon S matrix for a waveguidecoupled to a local quantum system that supports multiple ground states. Thepresence of the multiple ground states results in a non-commutative aspect ofthe system with respect to the exchange of the orders of photons. Consequently,the two-photon S matrix significantly differs from the standard form asdescribed by the cluster decomposition principle in the quantum field theory.

General structure of two-photon S matrix in waveguide quantum electrodynamics systems containing a local quantum system with multiple ground states