This paper offers a multiple surprise.

Firstly, its authors mention that the two-level evolution eq. (4)
of their state-of-the-art-review section 2 is pseudo-Hermitian.
This is the first, less important surprise: they do not pay any
attention to the amazing fact that both the mathematical and
physical origin of THIS equation (taken from refs. [24] and [25]
published in 1987 and 1988, respectively) is more than TEN years
older than ANY of the papers [1] - [17] on the use of
pseudo-Hermitian generators of the time evolution in physics which
the paper cites as a ``motivation" in section 1.

The latter observation offers, implicitly, not only a new view of
the history of PT symmetry and pseudo-Hermiticity but, in a
broader methodical context, also a sad illustration of the current
citation practice in science which starts to be characterized by
the very frequent occurrence of virtually complete loss of the
contact with all the relevant publications which happened to be
``too old" (i.e., say, older than ten years), with ideas being
``re-discovered" again and again.

The second surprise is the highly innovative character of the
subsequent message delivered in sections 3 and 4, viz., a compact
PSEUDO-HERMITIAN extension of the construction of the coherent
states (numbered by the complex Grassmann variables), described in
a way inspired by the ``traditional", Hermiticity-requiring
construction pattern (cf. refs. [33] - [35] and [37]).

In a certain synthesis of my two remarks I must admit that I also
belong to those who do forget: unfortunately, I cannot find a
preprint where, as far as I can remember, a construction of
pseudo-Hermitian coherent states has been proposed by Pinaki Roy
with some co-author.




MR2305317 Cherbal, O.; Drir, M.; Maamache, M.; Trifonov, D. A.
Fermionic coherent states for pseudo-Hermitian two-level systems.
J. Phys. A 40 (2007), no. 8, 1835--1844. 81R30