  We demonstrate the extension to PT-symmetric field theories of the Goldstone
theorem, confirming that the spontaneous appearance of a field vacuum
expectation value via minimisation of the effective potential in a
non-Hermitian model is accompanied by a massless scalar boson. Laying a basis
for our analysis, we first show how the conventional quantisation of the
path-integral formulation of quantum field theory can be extended consistently
to a non-Hermitian model by considering PT conjugation instead of Hermitian
conjugation. The extension of the Goldstone theorem to a PT-symmetric field
theory is made possible by the existence of a conserved current that does not,
however, correspond to a symmetry of the non-Hermitian Lagrangian. In addition
to extending the proof of the Goldstone theorem to a PT-symmetric theory, we
exhibit a specific example in which we verify the existence of a massless boson
at the tree and one-loop levels.
