On a c-number quantum $τ$-function

Details On a c-number quantum $τ$-function On a c-number quantum $τ$-function

1993-12-31

arxiv.org/abs/hep-th/9312213v2

Theor.Math.Phys.100:890-899,1995; Teor.Mat.Fiz.100:119-131,1994

Physics

High Energy Physics

High Energy Physics - Theory

12 pages, ITEP M-8/93, FIAN/TD-22/93, CRM-1934 (minor changes)

Scientific paper

10.1007/BF01017328

We first review the properties of the conventional $\tau$-functions of the KP and Toda-lattice hierarchies. A straightforward generalization is then discussed. It corresponds to passing from differential to finite-difference equations; it does not involve however the concept of operator-valued $\tau$-function nor the one associated with non-Cartanian (level $k\ne1$) algebras. The present study could be useful to understand better $q$-free fields and their relation to ordinary free fields.

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