Is there nematic liquid crystal system where the directors have Franks free energy with vector potentials?
Do mean that the director is a vector potential? Can you clarify what you mean by vector potential?
I didnt meant about that director is a vector potential. In the context of electromagnetic theory a vector potential is added to describe the kinetics of charged matter related to the energy and momentum. In this way is there any vector potential in liquid crystal so that one can add to the dynamics of liquid crystal.
If you take a look at P. G. DE Gennes' book (Chapter 10, page 511), you can notice that based on the analogy he made between smectic liquid crystals and superconductors, the magnetic vector potential for superconductor is analogous to small variation of smectic director in x and y direction. Therefore the vector potential is delta(n). Attached you can find extra info.
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