Integrable Chiral Quantum Field Theories with Spacetime-Dependent Interactions

We construct a class of integrable chiral fermionic quantum field theories with interactions depending on both space and time. The construction starts with a unitary, regular, difference-form two-body scattering matrix that satisfies braiding unitarity and the Yang–Baxter equation. Each freely moving right- or left-moving particle carries a characteristic coordinate that remains constant along its trajectory, and the scattering matrix depends on differences of these coordinates. The many-body amplitudes form a discrete connection over coordinate-ordering sectors. The Yang–Baxter equation gives its local flatness, while periodicity on a spatial circle produces quantum Knizhnik–Zamolodchikov difference equations expressing global flatness. In terms of a reference amplitude satisfying the exchange and qKZ constraints, these transports determine the exact fixed-particle-number wavefunction. We derive the characteristic form of the spacetime-dependent interaction and illustrate the construction with a chiral $SU(2)$ Gross–Neveu realization. Independent reparametrizations of the right- and left-moving characteristics yield genuine space-time dependence, whereas equal-slope affine maps recover the spatially homogeneous, time-dependent case.