Integrable Chiral Quantum Field Theories with Spacetime-Dependent Interactions

arXiv:2609.13377v1 Announce Type: cross 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.

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.

High Energy Physics - Theory (hep-th); Strongly Correlated Electrons (cond-mat.str-el); Mathematical Physics (math-ph); Exactly Solvable and Integrable Systems (nlin.SI); Quantum Physics (quant-ph)

arXiv:2609.13377 [hep-th]

(or arXiv:2609.13377v1 [hep-th] for this version)

https://doi.org/10.48550/arXiv.2609.13377 arXiv-issued DOI via DataCite (pending registration)

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Integrable Chiral Quantum Field Theories with Spacetime-Dependent Interactions

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