Multi-particle scattering states are constructed for massive Wigner particles in the general operator-algebraic setting of wedge-local quantum field theory. The apparent geometrical restriction of the conventional wedge-local Haag-Ruelle argument to two-particle scattering states is overcome with a swapping symmetry argument based on wedge duality. *

We develop Haag-Ruelle scattering theory for Wigner particles in local relativistic Quantum Field Theory without assuming mass gaps or any other restrictions on the spectrum of the mass operator near the particle masses. Our approach is based on the Reeh-Schlieder property of the vacuum state. It is shown that a strengthened variant of this property, concerning the relative approximation error for single-particle states, implies the existence of scattering states.

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A recently developed n-particle scattering theory for wedge-local quantum field theories is applied to a class of models described and constructed by Grosse, Lechner, Buchholz, and Summers. In the BLS-deformation setting we establish explicit expressions for n-particle wave operators and the S-matrix of ordered asymptotic states, and we show that ordered asymptotic completeness is stable under the general BLS-deformation construction. In particular the (ordered) Grosse-Lechner S-matrices are non-trivial also beyond two-particle scattering and factorize into 2-particle scattering processes, which is an unusual feature in space-time dimension d > 1 + 1. Most notably, the Grosse-Lechner models provide the first examples of relativistic (wedge-local) QFT in space-time dimension d > 1 + 1 which are interacting and asymptotically complete.

Using a BCS mean-field approach, we show how the interplay between low-momentum optical phonons and Jahn-Teller-type lattice distortions can open an attractive channel that allows the formation of pairs with the corresponding density exhibiting characteristic features of a pair-density wave (PDW). We demonstrate this numerically on a copper-oxide type lattice.