Point interactions in one dimension and holonomic quantum fields
arXiv:math-ph/0510095 · doi:10.1007/s11005-006-0081-7
Abstract
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 -bundle over a Grassmannian associated to a family of Schroedinger operators.
17 pages