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!

This post imported from StackExchange Physics at 2014-06-04 11:37 (UCT), posted by SE-user Idear