  A Bessel field $\mathcal{B}=\{\mathcal{B}(\alpha,t), \alpha\in\mathbb{N}_0,
t\in\mathbb{R}\}$ is a two-variable random field such that for every
$(\alpha,t)$, $\mathcal{B}(\alpha,t)$ has the law of a Bessel point process
with index $\alpha$. The Bessel fields arise as hard edge scaling limits of the
Laguerre field, a natural extension of the classical Laguerre unitary ensemble.
It is recently proved in [LW21] that for fixed $\alpha$,
$\{\mathcal{B}(\alpha,t), t\in\mathbb{R}\}$ is a squared Bessel Gibbsian line
ensemble. In this paper, we discover rich integrable structures for the Bessel
fields: along a time-like or a space-like path, $\mathcal{B}$ is a
determinantal point process with an explicit correlation kernel; for fixed $t$,
$\{\mathcal{B}(\alpha,t),\alpha\in\mathbb{N}_0\}$ is an exponential Gibbsian
line ensemble.
