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.
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.
- 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.
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