Point interactions in one dimension and holonomic quantum fields

We introduce and study a family of quantum fields, associated to delta-interactions in one dimension. These fields are analogous to holonomic quantum fields of M. Sato, T. Miwa and M. Jimbo. Corresponding field operators belong to an infinite-dimensional representation of the group SL(2,\Rb) in the Fock space of ordinary harmonic oscillator. We compute form factors of such fields and their correlation functions, which are related to the determinants of Schroedinger operators with a finite number of point interactions. It is also shown that these determinants coincide with tau functions, obtained through the trivialization of the $\mathrm{det}^*$-bundle over a Grassmannian associated to a family of Schroedinger operators.Comment: 17 page