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On the commuting charges and the Bethe ansatz for the quantised Kadomtsev-Petviashvili equation

  • Chiara Paletta
  • Alessandro Torrielli
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Abstract

We study the quantised version of the Kadomtsev-Petviashvili equation in the formulation proposed in [4]. We analyse two aspects. One is the conservation of the first higher charge H3 (besides the total mass H0, the momentum H1 and the Hamiltonian H2). We find the expression of H3 and prove commutativity, provided we regularise a specific ultraviolet divergence. The result then does not depend on the choice of a regulator, under fairly general assumptions. We then study the Bethe ansatz in finite volume and obtain a general solution to the two-body problem. We have used AI supervised by us to aid the proofs.

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Cite

BibTeXRIS
BibTeX
@misc{paletta2026commuting,
  title = {{On the commuting charges and the Bethe ansatz for the quantised Kadomtsev-Petviashvili equation}},
  author = {Chiara Paletta and Alessandro Torrielli},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.15316},
  eprint = {2609.15316},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.15316},
}
RIS
TY  - UNPB
TI  - On the commuting charges and the Bethe ansatz for the quantised Kadomtsev-Petviashvili equation
AU  - Chiara Paletta
AU  - Alessandro Torrielli
PY  - 2026
DA  - 2026/09/14
PB  - arXiv
DO  - 10.48550/arxiv.2609.15316
UR  - https://arxiv.org/abs/2609.15316
AB  - We study the quantised version of the Kadomtsev-Petviashvili equation in the formulation proposed in [4]. We analyse two aspects. One is the conservation of the first higher charge H_3 (besides the total mass H_0, the momentum H_1 and the Hamiltonian H_2). We find the expression of H_3 and prove commutativity, provided we regularise a specific ultraviolet divergence. The result then does not depend on the choice of a regulator, under fairly general assumptions. We then study the Bethe ansatz in finite volume and obtain a general solution to the two-body problem. We have used AI supervised by us to aid the proofs.
ER  -