  For a one-dimensional super-Brownian motion with density $X(t,x)$, we
construct a random measure $L_t$ called the boundary local time which is
supported on $\partial \{x:X(t,x) = 0\} =: BZ_t$, thus confirming a conjecture
of Mueller, Mytnik and Perkins (2017). $L_t$ is analogous to the local time at
$0$ of solutions to an SDE. We establish first and second moment formulas for
$L_t$, some basic properties, and a representation in terms of a cluster
decomposition. Via the moment measures and the energy method we give a more
direct proof that $\text{dim}(BZ_t) = 2-2\lambda_0> 0$ with positive
probability, a recent result of Mueller, Mytnik and Perkins (2017), where
$-\lambda_0$ is the lead eigenvalue of a killed Ornstein-Uhlenbeck operator
that characterizes the left tail of $X(t,x)$. In a companion work, the author
and Perkins use the boundary local time and some of its properties proved here
to show that $\text{dim}(BZ_t) = 2-2\lambda_0$ a.s. on $\{X_t(\mathbb{R}) > 0
\}$.
