一维点相互作用与完整量子场
Point interactions in one dimension and holonomic quantum fields
摘要：
我们介绍和研究了一个家庭的量子场，在一维的三角洲相互作用。这些场类似于M的完整量子场。佐藤，T. Miwa和M.吉姆相应的场算符属于群$SL(2,\Rb)$在普通谐振子Fock空间的无限维表示。我们计算了这些场的形状因子和它们的关联函数，这些函数与具有有限个点相互作用的薛定谔算子的行列式有关。它还表明，这些决定因素与τ函数相吻合，通过平凡化的$\mathrm{det}^*$ -丛在一个Grassmannian相关的一个家庭的薛定谔运营商。
英文摘要：
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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