2005/10/30 by O. Lisovyy · 1 citation
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Quantum chaos and dynamical systems #Theoretical and Computational Physics #math-ph #math.MP
paper · pdf · doi:10.1007/s11005-006-0081-7
published as Lett.Math.Phys.77:63-81,2006 · 17 pages
arxiv created 2005/10/30 · openalex publication_date 2006/04/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
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 det^*-bundle over a Grassmannian associated to a family of Schroedinger operators.