Time-dependent integrable quantum field theories with dynamical boundaries

@misc{kattel2026timedependent,
  title = {{Time-dependent integrable quantum field theories with dynamical boundaries}},
  author = {Pradip Kattel},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.03870},
  eprint = {2610.03870},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.03870},
  note = {CC BY 4.0},
}

TY  - UNPB
TI  - Time-dependent integrable quantum field theories with dynamical boundaries
AU  - Pradip Kattel
PY  - 2026
DA  - 2026/10/15
PB  - arXiv
DO  - 10.48550/arxiv.2610.03870
UR  - https://arxiv.org/abs/2610.03870
AB  - We present a general method to construct and solve time-dependent integrable chiral quantum field theories on finite intervals from autonomous scattering and reflection data. Spatial homogeneity forces the spectral labels of right- and left-moving particles to be affine with a common slope, so bulk and boundary couplings sample one spectral trajectory. A complete round trip shifts the spectral labels and gives boundary quantum Knizhnik--Zamolodchikov equations. The Yang--Baxter and reflection equations provide local consistency, while boundary-qKZ flatness provides global consistency. We reconstruct the local Hamiltonian by Cayley inversion of the bulk and boundary matching matrices. We apply the construction to rational SU(N) scattering with fundamental boundary impurities and to an O(3) model with a spin-1/2 impurity. For the SU(2) impurity, we construct explicit boundary-qKZ solutions as lattice sums of off-shell boundary Bethe vectors and recover the static open-chain Bethe equations when the drive rate vanishes
ER  -