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Updated: Sep 23, 2025

Vibrational Spectra of a N719-Chromophore/Titania Interface from Empirical-Potential Molecular-Dynamics Simulation, Solvated by a Room Temperature Ionic Liquid
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Embeddings and Integrable Charges for Extended Corner Symmetry.

Luca Ciambelli1, Robert G Leigh2, Pin-Chun Pai2

  • 1Physique Mathématique des Interactions Fondamentales & International Solvay Institutes, Université Libre de Bruxelles, Campus Plaine - CP 231, 1050 Bruxelles, Belgium.

Physical Review Letters
|May 16, 2022
PubMed
Summary
This summary is machine-generated.

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We extend the phase space of diffeomorphism-invariant theories by carefully treating embeddings. This introduces integrable, though not necessarily conserved, Noether charges for corner symmetries, representing them via Poisson brackets without central extension.

Area of Science:

  • Theoretical Physics
  • Mathematical Physics
  • Diffeomorphism-Invariant Theories

Background:

  • The covariant phase space formalism is crucial for understanding gauge theories.
  • Extending phase space to include boundary embeddings is a complex challenge.
  • Noether charges are fundamental to conserved quantities in physics.

Purpose of the Study:

  • To carefully treat embeddings in the covariant phase space formalism.
  • To introduce a new notion of extended field space.
  • To analyze the properties of Noether charges associated with extended corner symmetries.

Main Methods:

  • Revisiting the phase space extension problem for diffeomorphism-invariant theories.
  • Emphasizing the role of embeddings in the covariant phase space formalism.

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  • Introducing and analyzing a new extended field space concept.

    • Main Results:

    • A new notion of extended field space is introduced.
    • Noether charges associated with extended corner symmetries are integrable.
    • These charges represent the extended corner symmetry via Poisson brackets without central extension.

    Conclusions:

    • Careful treatment of embeddings is vital for covariant phase space formalism.
    • The proposed extension yields integrable Noether charges for corner symmetries.
    • The findings offer a new perspective on symmetries and charges in theoretical physics.