On to part 2, Duality!
Strings can wrap around a compact dimension, which leads to a number w, the ‘winding number’ of the string. Classically one would expect that to be fixed, but when we get interactions w will be able to change, i.e. be dynamic, and will have a corresponding quantum number.
Huggett goes on to explain T-duality. Winding and momentum can change roles (n <–> w) in the Hamiltonian (and R <–> 1/R) . The dynamics of the spatial wavefunction becomes the dynamics of the winding wavefunction in the dual, and vice-versa… the pattern of observed quantities is preserved. T-duality is like a translation manual between two theories.
This raises Huggett’s 3rd question: How should we understand T-duality? Do duals describe physically distinct situations?