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Letters in Mathematical Physics

, Volume 77, Issue 1, pp 63–81 | Cite as

Point Interactions in One Dimension and Holonomic Quantum Fields

  • Oleg Lisovyy
Article

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 Sato et al. in Holonomic quantum fields I–V (Publ. RIMS, Kyoto University, 14: 223–267, 1978; 15: 201–278, 1979; 15: 577–629, 1979; 15: 871-972, 1979; 16: 531–584, 1979). Corresponding field operators belong to an infinite-dimensional representation of the group \(SL(2,\mathbb{R})\) 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.

Keywords

point interactions Schroedinger operators tau functions 

Mathematics Subject Classification (2000)

34B10 34M55 

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Copyright information

© Springer 2006

Authors and Affiliations

  1. 1.Bogolyubov Institute for Theoretical PhysicsKyivUkraine
  2. 2.School of Theoretical PhysicsDublin Institute for Advanced StudiesDublin 4Ireland

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