  We present a brief derivation of the kinetic equation describing the secular
evolution of point vortices in two-dimensional hydrodynamics, by relying on a
functional integral formalism. We start from Liouville's equation which
describes the exact dynamics of a two-dimensional system of point vortices. At
the order ${1/N}$, the evolution of the system is characterised by the first
two equations of the BBGKY hierarchy involving the system's 1-body distribution
function and its 1-body correlation function. Thanks to the introduction of
auxiliary fields, these two evolution constraints may be rewritten as a
functional integral. When functionally integrated over the 2-body correlation
function, this rewriting leads to a new constraint coupling the 1-body
distribution function and the two auxiliary fields. Once inverted, this
constraint provides, through a new route, the closed non-linear kinetic
equation satisfied by the 1-body distribution function. Such a method sheds new
lights on the origin of these kinetic equations complementing the traditional
derivation methods.
