I am sorry that I did not sound understandable in my pervious questions.
There is a stringy version i.e. categorical version of the classical (non-quantum) physics situation in which a test massive and charge relativistic point particle is moving in an external electromagnetic field.
An example of the above mentioned situation is a closed bosonic string moving in an external H-field, a field whose potential is so-called B-field (2-connection of principal U(1)-gerbe) (see pages 20-24 of Chris Rogers' paper).
I would like to inform you that there is also a notion of (classical and quantum) relativistic harmonic oscillator:
I would like to ask if you could tell me whether or not mathematicians or mathematical physicists have already formulated a stringy version i.e. categorical version of a classical relativistic harmonic oscillator. If that is the case, than it would be interesting to see what a supersymmetric extensions and quantization of such construction would be.