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The partial Hamiltonian analysis of the actions presented in the paper by M.Chaichian, M. Oksanen, A. Tureanu (Eur. Phys. J. C 71, 1657 (2011)) isincorrect; the true algebra of constraints differs from what they claim fortheir choice of momentum constraint. Our blind acceptance of the correctness oftheir constraint algebra led us to conclude, wrongly, that a few of the modelspresented by the authors (sharing the same constraint algebra) are notinvariant under spatial diffeomorphism. We "proved" this by using Noether'ssecond theorem (see first version of the paper), but we then found a mistake inour calculations. The differential identity of spatial diffeomorphism isintact, therefore, their actions are invariant; but in this case, the spatialdiffeomorphism gauge symmetry cannot be compatible with their algebra. We nowexplicitly demonstrate that the actual algebra of constraints is different, andbriefly describe how it affects the generator and gauge transformations of thefields.

Comment on "Arnowitt--Deser--Misner representation and Hamiltonian  analysis of covariant renormalizable gravity" by M. Chaichian, M. Oksanen, A.  Tureanu