  Perturbative PT-symmetric quantum field theories with anti-Hermitian and
P-odd interaction terms are studied in path integral formalism and the i phi^3
model is calculated in detail. The nonlocal field transformation induced by the
C operator and corresponding transformations to Hermitian theories are given
systematically, which are manifestly 4-dimensional invariant. It is found that
the i phi^3 model can be transformed into infinitely many physically
inequivalent Hermitian theories with different S matrices under above nonlocal
transformations. Similar problem caused by nonlocal tranformations in Hermitian
quantum field theories is also discussed. 0-dimensional models are studied
numerically to verify the validity of those transformations. We put forward the
question of physical meaning of PT-symmetric quantum field theory based on the
arbitrariness caused by the seemingly inevitable nonlocality.
