  While the notion of open quantum systems is itself old, most of the existing
studies deal with quantum mechanical systems rather than quantum field
theories. After a brief review of field theoretical/path integral tools
currently available to deal with open quantum field theories, we go on to apply
these tools to an open version of $\phi^3$ + $\phi^4$ theory in four spacetime
dimensions and demonstrate its one loop renormalizability (including the
renormalizability of the Lindblad structure).
