Relation between a Screened Polyelectrolyte and a Field Theory

Abstract

There exists a generic relationship between the thermodynamics of a continuous polymer with a generic self-interaction and the two-point function of an interacting field-theory. In addition, the (2N)-point function of the resulting field theory is similarly related to a system of N interacting polymers. In the present paper, this relation is explored for the special case of a polyelectrolyte, characterized by a screened Coulomb pair potential. The corresponding field theory can be recast in a particularly simple form, corresponding to a quantum-mechanical particle, self-interacting via the emission and absorption of a massive scalar field. This is particularly useful in a perturbative treatment: perturbative expansions for the polyelectrolyte can be simply derived from the loop expansion for the related field-theoretical two-point function, for which established computational methods exist.