Point Interactions in One Dimension and Holonomic Quantum Fields

Lisovyy, Oleg (2006) Point Interactions in One Dimension and Holonomic Quantum Fields. Letters in Mathematical Physics, 77 (1). pp. 63-81. ISSN 0377-9017

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Abstract

We introduce and study a family of quantum fields, associated to δ-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,R) 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.

Item Type:	Article
Uncontrolled Keywords:	point interactions, Schroedinger operators, tau functions
Divisions:	School of Theoretical Physics > Preprints
Date Deposited:	05 Oct 2017 19:31
Last Modified:	18 Dec 2022 03:03
URI:	https://dair.dias.ie/id/eprint/174

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