  We use a perturbative momentum shell renormalization group (RG) approach to
study the properties of a driven quantum system at zero temperature. To
illustrate the technique, we consider a bosonic $\phi^4$ theory with an
arbitrary time dependent interaction parameter $\lambda(t)=\lambda f(\omega_0
t)$, where $\omega_0$ is the drive frequency and derive the RG equations for
the system using a Keldysh diagrammatic technique. We show that the scaling of
$\omega_0$ is analogous to that of temperature for a system in thermal
equilibrium and its presence provides a cutoff scale for the RG flow. We
analyze the resultant RG equations, derive an analytical condition for such a
drive to take the system out of the gaussian regime, and show that the onset of
the non-gaussian regime occurs concomitantly with appearance of
non-perturbative mode coupling terms in the effective action of the system. We
supplement the above-mentioned results by obtaining them from equations of
motions of the bosons and discuss their significance for systems near critical
points described by time-dependent Landau-Ginzburg theories.
