  The twisted Ruelle zeta function of a contact, Anosov vector field is shown
to be equal, as a meromorphic function of the complex parameter
$\hbar\in\mathbb{C}$ and up to a phase, to the partition function of an
$\hbar$-linear quadratic perturbation of $BF$ theory, using an "axial" gauge
fixing condition given by the Anosov vector field. Equivalently, it is also
obtained as the expectation value of the same quadratic, $\hbar$-linear,
perturbation, within a perturbative quantisation scheme for $BF$ theory,
suitably generalised to work when propagators have distributional kernels.
