Integrable Chiral Quantum Field Theories with Spacetime-Dependent Interactions
Abstract
We construct a class of integrable chiral fermionic quantum field theories with interactions that depend on both space and time. The construction starts from a unitary, regular, difference-form two-body scattering matrix satisfying 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 the coordinate-ordering sectors. The Yang--Baxter equation gives local path independence, while periodic winding on a spatial circle produces quantum Knizhnik--Zamolodchikov (qKZ) difference equations expressing global flatness. Once a reference amplitude satisfying the exchange and qKZ constraints is specified, these transport equations determine the exact wavefunction in every fixed-particle-number sector. Independent reparametrizations of the right- and left-moving characteristics give couplings that depend on both space and time. For the chiral SU(2) Gross--Neveu realization, we solve the qKZ equations for this full characteristic family using off-shell Bethe vectors. The resulting amplitudes are written in the characteristic labels, and their pullbacks give exact many-body wavefunctions for the corresponding space-time-dependent couplings. The two-body amplitude is a ratio of Gamma functions that resums the phase shifts from successive scattering processes. Equal-slope affine maps give a spatially homogeneous specialization in which the coupling depends only on time, and the Bethe ansatz with constant coupling is recovered when the qKZ step vanishes.
Related
- Time-dependent integrable quantum field theories with dynamical boundaries
- Elliptic spin Ruijsenaars-Schneider integrable models from 5d 𝒩=1 gauge theories
- Boundary Quantum Knizhnik-Zamolodchikov Equations and Integrability of Quantum Field Theories with Time-Dependent Bulk and Boundary Coupling Strengths
- Dynamic Vacuum Energy in Weyl Integrable Spacetime Part I: Implications for Inflationary Cosmology
- Correlation functions of the 19-vertex IRF model and its integrable quantum spin-1 chain
BibTeX
@misc{kattel2026integrable,
title = {{Integrable Chiral Quantum Field Theories with Spacetime-Dependent Interactions}},
author = {Pradip Kattel},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.13377},
eprint = {2609.13377},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.13377},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Integrable Chiral Quantum Field Theories with Spacetime-Dependent Interactions
AU - Pradip Kattel
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2609.13377
UR - https://arxiv.org/abs/2609.13377
AB - We construct a class of integrable chiral fermionic quantum field theories with interactions that depend on both space and time. The construction starts from a unitary, regular, difference-form two-body scattering matrix satisfying 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 the coordinate-ordering sectors. The Yang--Baxter equation gives local path independence, while periodic winding on a spatial circle produces quantum Knizhnik--Zamolodchikov (qKZ) difference equations expressing global flatness. Once a reference amplitude satisfying the exchange and qKZ constraints is specified, these transport equations determine the exact wavefunction in every fixed-particle-number sector. Independent reparametrizations of the right- and left-moving characteristics give couplings that depend on both space and time. For the chiral SU(2) Gross--Neveu realization, we solve the qKZ equations for this full characteristic family using off-shell Bethe vectors. The resulting amplitudes are written in the characteristic labels, and their pullbacks give exact many-body wavefunctions for the corresponding space-time-dependent couplings. The two-body amplitude is a ratio of Gamma functions that resums the phase shifts from successive scattering processes. Equal-slope affine maps give a spatially homogeneous specialization in which the coupling depends only on time, and the Bethe ansatz with constant coupling is recovered when the qKZ step vanishes.
ER -