  We calculate the dispersion of the out-of-phase mode characteristic for the
bilayer nu = 1 quantum Hall system applying the version of Chern-Simons theory
of Murthy and Shankar that cures the unwanted bare electron mass dependence in
the low-energy description of quantum Hall systems. The obtained value for the
mode when d, distance between the layers, is zero is in a good agreement with
the existing pseudospin picture of the system. For d nonzero but small we find
that the mode is linearly dispersing and its velocity to a good approximation
depends linearly on d. This is in agreement with the Hartree-Fock calculations
of the pseudospin picture that predicts a linear dependance on d, and contrary
to the naive Hartree predictions with dependence on the square-root of d. We
set up a formalism that enables one to consider fluctuations around the found
stationary point values. In addition we address the case of imbalanced layers
in the Murthy-Shankar formalism.
