Point interactions in one dimension and holonomic quantum fields

Details Point interactions in one dimension and holonomic quantum fields Point interactions in one dimension and holonomic quantum fields

2005-10-30

arxiv.org/abs/math-ph/0510095v1

Lett.Math.Phys.77:63-81,2006

Physics

Mathematical Physics

17 pages

Scientific paper

10.1007/s11005-006-0081-7

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.

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