First referee's report

Interesting work in this area.


Second referee's report

Dear Editor,

In this work the author outlines what might be the first steps of
a geometrical formulation of constrained systems at quantum level.
Although the work contais some interesting ideas, the presentation
is not suitable to be published in CQG. Specifically, the subjec
of constrained dynamics is plenty of simple examples of different
types of constraints at quantum and clasical level, thus we can
not understand why the author, who is suggesting a new definition
of physical states and observables, has not presented any
explicite example of application. In particular, no explicite
comparisson is made to the usual definitions in specific examples.


The author might consider to include few examples and, depending
on the results obtained of course, to write another work to be
submitted. He could also wonder if his presentation is not too
optimistic. He always presents the "first non trivial" condition
on observables but makes no comment on the importance of the
others (infinite ones). Besides, the master constraint does not
appear as natural as the author claims, in principle any
combination of square of the individual constraints, not only a
definite positive one, can be shown to hold starting from the
definition of physical state suggested here which must be applied
to each constraint separately.


Third referee's report

In this paper the author tries to find the `best' quantum
condition corresponding to a classical constraint. He reviews
basic results about classical constrained systems and also about
the geometric formulation of quantum systems. Then he proposes
that the quantum condition corresponding to a classical constraint
$C=0$ is the equation $(\Psi | \hat C^2 | \Psi) = 0.$ Then he
argues that an observable must have a vanishing double commutator
with $\hat C^2.$ The paper is clearly written and should be
published.


Board Member's report

I think this is a very good paper, which makes an important point,
so far overlooked, in the the quantum theory of constained
systems.