Generalized Coordinate Bethe Ansatz and Quantum Integrability of the Time-Dependent Massive Thirring Model
Abstract
We develop a generalized coordinate Bethe-ansatz framework for the massive Thirring model with an explicitly time-dependent fermion mass. Unlike the generalized Bethe ansatz for chiral quantum field theories, where particle transport acts in internal spin spaces and leads to quantum Knizhnik-Zamolodchikov equations, the present construction acts directly on particle coordinates and physical rapidities. Its central new feature is a rapidity lattice. Because the time-dependent mass couples right- and left-moving components already in the one-particle sector, a fixed-rapidity block is not closed under spatial winding. Periodicity therefore requires all sectors generated by the finite shift β→β−p. Particle exchange relates amplitudes on this lattice through scalar analytic difference equations of Ruijsenaars type, whose solutions determine the complete time-dependent many-body wavefunction. Consistency of the coordinate construction also selects an exponential evolution of the bare mass, providing a new realization of the time dependent integrability-renormalization group correspondence. In the static limit, the rapidity-lattice construction reduces to the conventional massive-Thirring Bethe equations. Through the massive-Thirring/sine Gordon equivalence, the result also connects this exact quantum construction to the generalized space-time dependent Lax formalism.
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BibTeX
@misc{pasnoori2026generalized,
title = {{Generalized Coordinate Bethe Ansatz and Quantum Integrability of the Time-Dependent Massive Thirring Model}},
author = {Parameshwar R. Pasnoori},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.29998},
eprint = {2610.29998},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.29998},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Generalized Coordinate Bethe Ansatz and Quantum Integrability of the Time-Dependent Massive Thirring Model
AU - Parameshwar R. Pasnoori
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.29998
UR - https://arxiv.org/abs/2610.29998
AB - We develop a generalized coordinate Bethe-ansatz framework for the massive Thirring model with an explicitly time-dependent fermion mass. Unlike the generalized Bethe ansatz for chiral quantum field theories, where particle transport acts in internal spin spaces and leads to quantum Knizhnik-Zamolodchikov equations, the present construction acts directly on particle coordinates and physical rapidities. Its central new feature is a rapidity lattice. Because the time-dependent mass couples right- and left-moving components already in the one-particle sector, a fixed-rapidity block is not closed under spatial winding. Periodicity therefore requires all sectors generated by the finite shift β→β−p. Particle exchange relates amplitudes on this lattice through scalar analytic difference equations of Ruijsenaars type, whose solutions determine the complete time-dependent many-body wavefunction. Consistency of the coordinate construction also selects an exponential evolution of the bare mass, providing a new realization of the time dependent integrability-renormalization group correspondence. In the static limit, the rapidity-lattice construction reduces to the conventional massive-Thirring Bethe equations. Through the massive-Thirring/sine Gordon equivalence, the result also connects this exact quantum construction to the generalized space-time dependent Lax formalism.
ER -