  This note is a reply to the paper arXiv:1801.05590: "The equivalence of the
Power-Zineau-Woolley picture and the Poincar{\'e} gauge from the very first
principles" by G. K{\'o}nya, et al.
  In a recent paper [2], we have shown that the Power-Zienau-Woolley
Hamiltonian does not derived from the minimal-coupling hamiltonian with the
help of a gauge transformation. This result has been challenged by G.
K{\'o}nya, al. in a comment 1 where the authors claim the equivalence between
the Power-Zienau-Woolley hamiltonian and the minimal-coupling hamiltonian in
the Poincar{\'e} gauge. They claim that we have made one error and one wrong
emphasis in our paper: The error as summarized by G. K{\'o}nya al. would be:
"The canonical field momentum is not gauge invariant. Equivalent
transformations of the Lagrangian do change the momentum. In field theories,
gauge transformations are special cases of such transformations. The electric
field E is gauge invariant, but its capacity of being the canonical momentum is
not. " The wrong emphasis as summarized by G.K{\'o}nya al. would be: "The use
of the canonical coordinate/momentum pair A p and E in Poincar{\'e} gauge is
presented as mandatory in Rousseau and Felbacq paper, whereas as there is a
certain freedom of choice in selecting this pair. Also in Poincar{\'e} gauge it
is possible to use A c as canonical coordinate, in which case the conjugate
momentum will be D. This is the most convenient choice in terms of the set of
nontrivial Dirac brackets. Cf. Table 1 in G. K{\'o}nya al. paper 1 for possible
choices."
  We do not share these conclusions and show in this reply that these
statements are incorrect. Specifically, we show that under a gauge
transformation, the canonical momentum $\pi$(x,t) conjugated to the vector
potential A(x,t) is given by $\pi$(x,t) = --$\epsilon$\_0 E(x,t). This happens
because the Lagrangian does not contains terms proportional to $\partial$\_t
$\phi$ (x,t) where $\phi$ (x,t) is the scalar potential. Moreover our choice of
canonical variables was challenged. Actually, our set of independent variables
is exactly the same as in G. K{\'o}nya al. except that we do not write
explicitly the dependent variables in term of the independent ones. This is one
great advantage of the Dirac procedure for constrained hamiltonian.
