Equilibrium correlation function in post-Galilean approximation of a scalar field

The exact formula for the equilibrium one-dimensional binary distribution function for scalar particles, interacting by the potential 1/r, is obtained in the post-Galilean approximation. To take into account the post-Galilean corrections (i.e. the values of the order of O(c−2), where c is the velocity of light), the temperature shift is suggested. It means that in this relativistic approximation we can use the classical coordinate distribution function with the shifted temperature parameter.