  The covariant phase space technique is a powerful formalism for understanding
the Hamiltonian description of covariant field theories. However, applications
of this technique to problems involving subregions, such as the exterior of a
black hole, have heretofore been plagued by boundary ambiguities. We provide a
resolution of these ambiguities by directly computing the symplectic structure
from the path integral, showing that it may be written as a contour integral
around a partial Cauchy surface. This result has implications for gauge
symmetry and entanglement.
