Referee's Report - Confidential
Referee: Gérard H. E. Duchamp................................................
Paper no.:..25...........................................
Title: ......Equivariant functions in topological quantum mechanics
Authors: Jan Milewski
Please see the attached "Checklist for Referees" as a guideline for your assessment.
1.        Recommendation regarding publication
X Publication in the present form (please give reasons on the following page). 
  Publication subject to minor amendments indicated in the report (further review not necessary).
  The author should be advised to revise the paper for resubmission (second review necessary).
        I am willing to review the revised version.
       I suggest as an alternative referee (please give communication details, if possible):
    The paper should be rejected without qualification.
3.        Evaluation of scientific content and clarity of presentation
Scientific content:      X Good         
Presentation:  X Good         
Language polishing required: X minor       
Hints for Editorial Office regarding manuscript editing (if not included in comments to
author):
Please support your recommendation with anonymized comments, suitable for transmission to the author, on the following page (also in the case of acceptance).
The paper  is interesting, but some passages seem to have been hastily written. Also, it would be desirable to have a bit more insights about the mathematical difficulties and hints of he proofs.
My overall impression remains very good and the paper should be accepted with only minor amendments (see next page).
Gérard H. E. Duchamp

Comments to author

Some suggestions for improvement (pn=page n, ln=line n, l-n= line n from bottom)

Abstract : [We deal in the paper with ]  [In the paper we deal with ]

1. Introduction : line 7 [configuration spac]   [configuration space]

Line 11 [Hamiltonians are not Hermitian ] [Hamiltonians are not necessarily hermitian ]

Line –6 [In Section 3 we consider]  [In Section 3, we consider]

Line –5 [the whole Hilbert space of squre-integrable]  [the whole Hilbert space of square-integrable]

2. Topological quantum mechanics 

Line 2 [fundametal]   [fundamental]

Line –5 (page 2) [Hermitean]  ) [hermitian] (without capital letter, it is an adjective)

(same line) [L^2(M,C,d\mu) the \hat T]  [L^2(M,C,d\mu) the operator \hat T]

3. Anyons in a plane

Page 5 line –5 : [what is identical formula with the second]  [which is a formula identical to the second]
Line –3 (page 6) [for anisotropic oscillator]  [for the anisotropic oscillator]

4. [Conclusion remarks ]  [Concluding remarks]

Please indent the first line.