Integrable Chiral Quantum Field Theories with Spacetime-Dependent Interactions

• URL: http://arxiv.org/abs/2609.13377v1
• Date: Fri, 11 Sep 2026 18:00:02 GMT
• Title: Integrable Chiral Quantum Field Theories with Spacetime-Dependent Interactions
• Abstract summary: We construct a class of integrable chiral fermionic quantum field theories with interactions depending on both space and time.<n>We derive the characteristic form of the spacetime-dependent interaction and illustrate the construction with a chiral $SU(2)$ Gross-Nevarity-eu realization.
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• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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