  I review the generating function for quantum-statistical mechanics, known as
the Feynman-Vernon influence functional, the decoherence functional, or the
Schwinger-Keldysh path integral. I describe a probability-conserving
$i\varepsilon$ prescription from a path-integral implementation of Lindblad
evolution. I also explain how to generalize the formalism to accommodate
out-of-time-ordered correlators (OTOCs), leading to a Larkin-Ovchinnikov path
integral. My goal is to provide step-by-step calculations of path integrals
associated to the harmonic oscillator.
