Covariant phase space with boundaries
| Autor: | Jie-qiang Wu, Daniel Harlow |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
High Energy Physics - Theory
Nuclear and High Energy Physics FOS: Physical sciences General Relativity and Quantum Cosmology (gr-qc) AdS-CFT Correspondence 01 natural sciences General Relativity and Quantum Cosmology Poisson bracket symbols.namesake 0103 physical sciences lcsh:Nuclear and particle physics. Atomic energy. Radioactivity Covariant transformation Peierls bracket Boundary value problem 010306 general physics Mathematical physics Physics Hamiltonian mechanics 010308 nuclear & particles physics Phase space method Equations of motion High Energy Physics - Theory (hep-th) Phase space symbols lcsh:QC770-798 Classical Theories of Gravity |
| Zdroj: | Journal of High Energy Physics Journal of High Energy Physics, Vol 2020, Iss 10, Pp 1-52 (2020) |
| DOI: | 10.48550/arxiv.1906.08616 |
| Popis: | The covariant phase space method of Iyer, Lee, Wald, and Zoupas gives an elegant way to understand the Hamiltonian dynamics of Lagrangian field theories without breaking covariance. The original literature however does not systematically treat total derivatives and boundary terms, which has led to some confusion about how exactly to apply the formalism in the presence of boundaries. In particular the original construction of the canonical Hamiltonian relies on the assumed existence of a certain boundary quantity "$B$", whose physical interpretation has not been clear. We here give an algorithmic procedure for applying the covariant phase space formalism to field theories with spatial boundaries, from which the term in the Hamiltonian involving $B$ emerges naturally. Our procedure also produces an additional boundary term, which was not present in the original literature and which so far has only appeared implicitly in specific examples, and which is already nonvanishing even in general relativity with sufficiently permissive boundary conditions. The only requirement we impose is that at solutions of the equations of motion the action is stationary modulo future/past boundary terms under arbitrary variations obeying the spatial boundary conditions; from this the symplectic structure and the Hamiltonian for any diffeomorphism that preserves the theory are unambiguously constructed. We show in examples that the Hamiltonian so constructed agrees with previous results. We also show that the Poisson bracket on covariant phase space directly coincides with the Peierls bracket, without any need for non-covariant intermediate steps, and we discuss possible implications for the entropy of dynamical black hole horizons. Comment: 61 pages, two figures. v2: improved referencing v3: minor improvements and references added v4: Journal version, minor clarifications and discussion of the initial value problem added |
| Databáze: | OpenAIRE |
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