The famous model of (quantum) field theory as proposed by T. D. Lee
in 1954 has originally been invented as an explicitly solvable,
oversimplified methodical laboratory admitting the closed-form
renormalization. In parallel, the model has almost immediately been
rejected as being NOT a consistent system exhibiting the standard
unitary evolution in time. This appeared to follow from the
detection of the presence of the zero- and negative-norm states
(``ghosts"). Recently (cf. the list of references), Bender with
coauthors spotted the error and clarified (while the abstracted
compact review paper summarizes the conclusion) that the ``ghosts"
will disappear (i.e., their norm will be made positive, making the
model unitary and compatible with the current textbook postulates)
just via a suitable redefinition of the linear functionals (i.e., in
other words, of the inner product in the amended, new, corrected,
physical Hilbert space of states). In the review paper under
consideration, the author shows that (and how) the product of the so
called ``parity" ${\cal P}$ of the model and of the so called
``charge" ${\cal C}$ of the model defines (one of) the correct
inner-product metrics, in the lowest nontrivial ``sector" (i.e.,
subspace) of the traditional Lee model at least.

MR2758898 Bender, Carl M. Ghost busting: making sense of
non-Hermitian Hamiltonians. Algebraic analysis of differential
equations from microlocal analysis to exponential asymptotics,
55--66, Springer, Tokyo, 2008. 81Q12