I have been informed that 1+1D Bosonization/Fermionization on a line segment or 1+1D Bosonization/Fermionization a compact ring are different -

Although I know that Bosonization can rewrite fermions in the non-local expression of bosons. But:

bosons and fermions are fundamentally different for the case of on a 1D compact ring.

Is this true? How is the Bosonization/Fermionization different on a line segment or a compact ring? Does it matter whether the line segment is finite $x\in[a,b]$ or infinite $x\in(-\infty,\infty)$? Why? Can someone explain it physically? Thanks!

  • 3
    I think, when people say line segment, they often mean an interval $[a,b]$. Regarding your question, my low-brow understanding is that the difference has to do with braiding. You cannot braid two (hard-core) bosons or fermions on a line segment, but you can on a ring. On a slightly more technical level, an example would be the Jordan-Wigner transformation for hard-core bosons. We need to be careful about boundary conditions when we do JW transformation on a ring. – Isidore Seville Mar 9 '14 at 1:54
  • Very good, Isidore, it totally makes sense. – wonderich Mar 9 '14 at 2:09

Your Answer

 

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Browse other questions tagged or ask your own question.