  Quantum systems governed by non-Hermitian Hamiltonians with $\PT$ symmetry
are special in having real energy eigenvalues bounded below and unitary time
evolution. We argue that $\PT$ symmetry may also be important and present at
the level of Hermitian quantum field theories because of the process of
renormalisation. In some quantum field theories renormalisation leads to
$\PT$-symmetric effective Lagrangians. We show how $\PT$ symmetry may allow
interpretations that evade ghosts and instabilities present in an
interpretation of the theory within a Hermitian framework. From the study of
examples $\PT$-symmetric interpretation is naturally built into a path integral
formulation of quantum field theory; there is no requirement to calculate
explicitly the $\PT$ norm that occurs in Hamiltonian quantum theory. We discuss
examples where $\PT$-symmetric field theories emerge from Hermitian field
theories due to effects of renormalization. We also consider the effects of
renormalization on field theories that are non-Hermitian but $\PT$-symmetric
from the start.
