Covariant phase space with boundaries

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• Daniel Harlow (MIT)
• Thursday 04 June 2020, 14:00-15:00
• Online (Zoom).

If you have a question about this talk, please contact Pietro Benetti Genolini.

The Hamiltonian formulation of mechanics has several decisive advantages: it gives a clear accounting of the physical degrees of freedom, the initial-value problem is naturally formulated, and the relationship to quantum mechanics is clear. On the other hand, as usually formulated it destroys manifest spacetime covariance and applies only to equations of motion with at most two derivatives. Both of these problems are avoided in the covariant phase space formalism, developed most notably by Wald and collaborators in the early 1990s. Their formalism however suffers from ambiguities related to total derivatives and boundary terms, which so far have been dealt with on an ad hoc case-by-case basis. This is especially unfortunate for gravitational theories, for which any nontrivial Hamiltonian will necessarily be a boundary term and thus boundary effects are of central importance. In this talk I will describe work with Jie-qiang Wu where we improve the covariant phase space formalism to systematically include boundary effects: the result is that for any Lagrangian field theory based on a local action with a finite number of derivatives, there is now a systematic, practical, and fully-covariant way to construct the phase space and Hamiltonian, as well as any other conserved charges. Moreover the approach is quite convenient in practice, for example it allows perhaps the most compact derivation so far of the ADM Hamiltonian.

This talk is part of the Quantum Fields and Strings Seminars series.

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