  We analyze the zero point energy of composite particles (or resonances) which
are dynamically created from relativistic fermions. We compare the zero point
energies in medium to the vacuum one, taking into account the medium
modification of the constituent particles. Treating composite particles as if
quasi-particles, their zero point energies contain the quadratic and
logarithmic UV divergences even after the vacuum subtraction. The coefficients
of these divergences come from the difference between the vacuum and in-medium
fermion propagators. We argue that such apparent divergences can be cancelled
by consistently using fermion propagators to compute the quasi-particle
contributions as well as their interplay, provided that the self-energies of
the constituents at large momenta approach to the vacuum ones sufficiently
fast. In the case of quantum chromodynamics, mesons and baryons, which may be
induced or destroyed by medium effects, yield the in-medium divergences in the
zero point energies, but the divergences are assembled to cancel with those
from the quark zero-point energy. This is particularly important for unified
descriptions of hadronic and quark matter which may be smoothly connected by
the quark-hadron continuity.
