Pointlike interactions in 1D quantum mechanics can be defined by certain self-adjoint extensions of the second derivative operator (d/dx)^2. According to a classification by Kurasov and Albeverio et al, the textbook "\delta potential" with coupling strength c is the unique pointlike interaction between bosons. Through the Girardeau mapping, it is dual to the less known unique pointlike interaction between fermions. I will prove that this fermionic pointlike interaction can be obtained as a limit of regular potentials that vanish when c\to\infty. This implements thus a strong-weak duality between bosons and fermions in 1D. I will present applications to the Lieb-Liniger model, a gas of particles interacting via the \delta potential.
Thomas Strobl
