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Peer-reviewedCC BY 4.0Journal of High Energy Physics

Poisson bracket and L∞ algebras

  • Vinícius Bernardes1
  • Theodore Erler1
  • Atakan Hilmi Fırat2
  • Igor Khavkine3
  1. 1CEICO, FZU – Institute of Physics of the Czech Academy of Sciences
  2. 2University of California
  3. 3Institute of Mathematics of the Czech Academy of Sciences
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Abstract

We describe the Poisson bracket of a Lagrangian field theory expressed in the framework of L∞ algebras. If the symplectic structure on phase space is defined following recent work, we show that the Poisson bracket can be computed with the Peierls formula, confirming the well-known result of the covariant phase space formalism. Of particular interest is the Poisson bracket in nonlocal theories. In p-adic string theory we find that a straightforward construction of the Poisson bracket is obstructed by higher derivative instabilities. We also discuss the inverse relation between the Poisson bracket and symplectic structure in the language of homological algebra, extending some ideas in the mathematical physics literature.

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Cite

BibTeXRIS
BibTeX
@article{bernardes2026poisson,
  title = {{Poisson bracket and L∞ algebras}},
  author = {Vinícius Bernardes and Theodore Erler and Atakan Hilmi Fırat and Igor Khavkine},
  journal = {Journal of High Energy Physics},
  year = {2026},
  month = nov,
  doi = {10.1007/jhep11(2026)049},
  url = {https://link.springer.com/article/10.1007/JHEP11(2026)049},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Poisson bracket and L∞ algebras
AU  - Vinícius Bernardes
AU  - Theodore Erler
AU  - Atakan Hilmi Fırat
AU  - Igor Khavkine
PY  - 2026
DA  - 2026/11/05
JO  - Journal of High Energy Physics
DO  - 10.1007/jhep11(2026)049
UR  - https://link.springer.com/article/10.1007/JHEP11(2026)049
AB  - We describe the Poisson bracket of a Lagrangian field theory expressed in the framework of L∞ algebras. If the symplectic structure on phase space is defined following recent work, we show that the Poisson bracket can be computed with the Peierls formula, confirming the well-known result of the covariant phase space formalism. Of particular interest is the Poisson bracket in nonlocal theories. In p-adic string theory we find that a straightforward construction of the Poisson bracket is obstructed by higher derivative instabilities. We also discuss the inverse relation between the Poisson bracket and symplectic structure in the language of homological algebra, extending some ideas in the mathematical physics literature.
SN  - 1029-8479
ER  -