Regularization of a strong-weak duality between pointlike interactions in one dimension

Pointlike interactions between bosons in 1D are related to pointlike interactions between fermions through the Girardeau mapping. This mapping is a strong-weak duality since the coupling constants in the bosonic and fermionic cases are inversely proportional to each other. We present a regularization of these pointlike interactions that preserves the strong-weak duality, contrary to previously known Hermitian regularizations. This is proven rigorously. This allows one to use this duality perturbatively and we illustrate it in the Lieb-Liniger model at strong coupling.

Automated summary

This article presents a regularization method for preserving the strong-weak duality of pointlike interactions, contrary to previous known regularizations. This allows perturbative use of the duality, which is illustrated in the Lieb-Liniger model at strong coupling.