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!