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The integer spectrum of a superintegrable quantum field theory — arXiv:2611.05015

Source: arXiv (en)
Original: https://arxiv.org/abs/2611.05015
License (as archived): CC0-1.0
Archived: 2026-11-04T19:01:43.187Z
SHA-256 of the archived text: a0ae91f3d4642ae20c896e2c47123855bffcc9a4bd313a70ab81d1651c40558d
Stable URL of this page: https://metraipolis.com/documento/dc_676b856437d4

How to cite

The integer spectrum of a superintegrable quantum field theory — arXiv:2611.05015 — arXiv (en), https://arxiv.org/abs/2611.05015 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_676b856437d4 (Metraipolis archive dc_676b856437d4, sha256 a0ae91f3d4642ae20c896e2c47123855bffcc9a4bd313a70ab81d1651c40558d)

BibTeX

@misc{dc676b856437d4,
  title = {The integer spectrum of a superintegrable quantum field theory — arXiv:2611.05015},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2611.05015},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_676b856437d4; sha256 a0ae91f3d4642ae20c896e2c47123855bffcc9a4bd313a70ab81d1651c40558d},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2611.05015. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

In our previous article CMP 407 (2026) 131, we explored the rich algebraic structures arising from a specific quantum many-body Hamiltonian quartic in the bosonic creation-annihilation operators. This Hamiltonian originated from the works of Gérard and Grellier on classical turbulent energy transfer in a Lax-integrable setting, and its quantum version respects hierarchies of polynomial conservation laws all of which possess purely integer spectra, as does the Hamiltonian itself. The latter feature, known from numerical studies, has previously remained unproved. Here, we present an elementary solution of the quantum Gérard-Grellier Hamiltonian. The eigenstates are labelled by partitions and the corresponding eigenvalues admit simple explicit expressions in terms of the principal hook lengths. The key ingredient in this construction is a specific basis we introduce, inspired by the classical multisoliton coherent states, in which the Hamiltonian is upper-triangular. The expressions for the eigenvalues then immediately follow, while the full eigenbasis can be recovered via a Gram-Schmidt procedure.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv math.CO, nuovi lavori del giorno).
Categorie arXiv: Exactly Solvable and Integrable Systems (nlin.SI) ; High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph); Analysis of PDEs (math.AP); Combinatorics (math.CO).
Pagina del lavoro: https://arxiv.org/abs/2611.05015 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-11-04T18:38:22.342Z dalla pagina https://arxiv.org/list/math.CO/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).