  While detailed information about the semiclassics for single-particle systems
is available, much less is known about the connection between quantum and
classical dynamics for many-body systems. As an example, we focus on spin
chains which are of considerable conceptual and practical importance. We derive
a trace formula for coupled spin $j$ particles which relates the quantum energy
levels to the classical dynamics. Our derivation is valid in the limit
$j\rightarrow\infty$ with $j\hbar={\rm const.}$ and applies to time-continuous
as well as to periodically driven dynamics. We provide a simple explanation why
the Solari-Kochetov phase can be omitted if the correct classical Hamiltonian
is chosen.
