Random Gaussian fields applied to fluctuating polymers and biopolymers, eg protein chains and DNA. First, non-conducting knotted charged strings or polymers in a non-conducting viscous fluid leads to the concept of knot energy functionals. The electrosatic energy will minimise without intersection due to Coulomb forces. One can then define a knot-energy funcional. Let be two such knots in a domain such that . Let and . A regulated knot energy functional is defined as

Similary, two knots carrying unit currents leads to the Bio-Savart law

Let be a random Gaussian vector field defined for all and with respect to a triplet . Then if:

The expectation of the stochastic Wilson line of gives

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if:

The expectation of the stochastic Wilson line of gives

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