A functional relation among the pair correlations of the two-dimensional one-component plasma

We map the classical two-dimensional one-component plasma of charged particles with coupling constant Γ an even positive integer onto a one-dimensional fermionic system. We then show that, in the thermodynamic limit of the fluid regime, translational invariance of the two-body density implies an infinite sequence of interrelations among the coefficients of its short-distance expansion. The existence of these sum rules turns out to be related to a general symmetry of the Coulomb system, providing a functional relation for the two-body density for arbitrary coupling Γ.