Christoph, I had nothing particular in mind. I simply find it hard to believe that of the thousands of people working on quantum theory, nobody has looked at fluctuating strands. I looked through arxiv, but did not find anything. There are many papers on the "polymer representation" of quantum theory, but they have nothing to do with your approach.I looked through the literature and did not find anything on the matter. I found some ideas on polymers and evolution equations similar to the Schrödinger equation, but nothing of the type you ask for. Of the people that tried to model wave functions, nobody seems to have though about strands and tangles - except of course, Battey-Pratt and Racey in 1980. But their ideas did not catch on. Racey wrote to me saying that they tried to ask Dirac about this, but Dirac never answered. What a pity!
Do you have something specific in mind?