We find a new vacuum of the Bethe ansatz solutions in the massless Thirring
model. This vacuum breaks the chiral symmetry and has the lower energy than the
well-known symmetric vacuum energy. Further, we evaluate the energy spectrum of
the one particle-one hole ($1p-1h$) states, and find that it has a finite gap.
The analytical expressions for the true vacuum as well as for the lowest
$1p-1h$ excited state are also found. Further, we examine the bosonization of
the massless Thirring model and prove that the well-known procedure of
bosonization of the massless Thirring model is incomplete because of the lack
of the zero mode in the boson field.Comment: 7 page
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.