Dirac equation is studied in the phenomenologically oriented
scattering regime where the relativistic unitarity-violating
creation and annihilation effects are simulated, as usual, via an
imaginary component in the effective square-well potential. These
results, highly interesting per se, acquired also an additional,
purely theoretical relevance briefly after their publication.
Indeed, once one does not insist on the presence of a charge-type
involution factor C in the metric $\Theta$ in the Hilbert space of
states (cf. also ref. [27] in this respect), the present
effective-theory results could acquire a parallel,
fundamental-theory reinterpretation in which the unitarity would not
be violated at all. This exciting possibility has been conjectured
in ref. [24] (to be updated as H. F. Jones, Phys. Rev. D 76, 125003
(2007), with a fresh thought a bit sceptical part II: H. F. Jones,
arXiv:0805.1656). In the subsequent final and entirely optimistic
update of the fundamental scattering theory based on PT-symmetric
and other ``cryptohermitian" interaction terms [cf. M. Znojil,
``Discrete PT-symmetric models of scattering", J. Phys. A41, 292002
(2008) and in M. Znojil, ``Scattering theory with localized
non-Hermiticities", Phys. Rev. D, to appear (arXiv:0805.2800v1
[hep-th] 19 May 2008)], the existence and necessary asymptotic
locality of the fully consistent physical metric $\Theta$ has
constructively been demonstrated.


MR2393586 Cannata, Francesco; Ventura, Alberto Overcritical
$\scr{PT}$-symmetric square well potential in the Dirac equation.
Phys. Lett. A 372 (2008), no. 7, 941--946. 81Q10