  We present an exact field theoretical representation of the statistical
mechanics of classical hard-core Coulomb systems. This approach generalizes the
usual sine-Gordon theory valid for point-like charges or lattice systems to
continuous Coulomb fluids with additional short-range interactions. This
formalism is applied to derive the equation of state of the restricted
primitive model of electrolytes in the low fugacity regime up to order
$\rho^{5/2}$ ($\rho$ number density). We recover the results obtained by Haga
by means of Mayer graphs expansions.
