  The accurate theoretical description of the dynamic properties of correlated
quantum many-body systems such as the dynamic structure factor
$S(\mathbf{q},\omega)$ constitutes an important task in many fields.
Unfortunately, highly accurate quantum Monte Carlo methods are usually
restricted to the imaginary time domain, and the analytic continuation of the
imaginary time density--density correlation function $F(\mathbf{q},\tau)$ to
real frequencies is a notoriously hard problem. In this work, we argue that no
such analytic continuation is required as $F(\mathbf{q},\tau)$ contains, by
definition, the same physical information as $S(\mathbf{q},\omega)$, only in an
unfamiliar representation. Specifically, we show how we can directly extract
key information such as the temperature or quasi-particle excitation energies
from the $\tau$-domain, which is highly relevant for equation-of-state
measurements of matter under extreme conditions. As a practical example, we
consider \emph{ab initio} path integral Monte Carlo results for the uniform
electron gas (UEG), and demonstrate that even nontrivial processes such as the
\emph{roton feature} of the UEG at low density straightforwardly manifest in
$F(\mathbf{q},\tau)$. In fact, directly working in the $\tau$-domain is
advantageous for many reasons and holds the enticing promise for unprecedented
agreement between theory and experiment.

Statistical Mechanics;Strongly Correlated Electrons;Quantum Physics