  In this work, we carry out a study of the conserved quantities and dynamical
structure of the four-dimensional modified axion electrodynamics theory
described by the axion-photon coupling. In the first part of the analysis, we
employ the covariant phase space method to construct the conserved currents and
to derive the Noether charges associated with the gauge symmetry of the theory.
We further derive the improved energy-momentum tensor using the
Belinfante-Rosenfeld procedure, which leads us to the expressions for the
energy, momentum, and energy flux densities. Thereafter, with the help of
Faddeev-Jackiw's Hamiltonian reduction formalism, we obtain the relevant
fundamental brackets structure for the dynamic variables and the functional
measure for determining the quantum transition amplitude. We also confirm that
modified axion electrodynamics has three physical degrees of freedom per space
point. Moreover, using this symplectic framework, we yield the gauge
transformations and the structure of the constraints directly from the
zero-modes of the corresponding presymplectic matrix.
