It is slightly puzzling that the postulates of nonrelativistic
Quantum Mechanics (which, by definition, deals with a finite
number of degrees of freedom or, if you wish, with moving
particles etc) preserve their form, unchanged, from their very
birth, i.e., for cca 80 years. In contrast, the virtually equally
old history of attempts of extending the formalism to cover the
domain of relativistic kinematics is still full of gaps and open
questions. As a result, one usually accepts quantum theory of
fields characterized,  as a rule, by infinitely many degrees of
freedom or, if you wish, by local excitations etc. With all its
well known imperfections it seems to be the only candidate for
description, say, of the motion of a single elementary particle
with zero spin. In textbooks you usually find the statement that
the natural (viz, Klein-Gordon-based) version of Quantum Mechanics
is ``inconsistent" as offering ``negative probabilities". The
latter (and, by the reviewed author's as well as by this
reviewer's opinion, wrong) common wisdom has been perceivably
shattered by Ali Mostafazadeh et al (the history has been briefly
outlined in the paper or in its ref. [26]) who noticed that a
redefinition of the Hilbert space (i.e., first of all, of its
inner product) simply solves the ``negative probability" puzzle so
that a standard Klein-Gordon Quantum Mechanics is obtained. The
paper under review extends and complements this important result
by showing how the formalism looks in the chargeless case of the
Klein-Gordon real field and how the whole theory fits in the so
called PT-symmetric Quantum Mechanics.

MR2257378 Kleefeld, Frieder On some meaningful inner product for
real Klein-Gordon fields with positive semi-definite norm.
Czechoslovak J. Phys. 56 (2006), no. 9, 999--1006. 81T10 (81Q10)