publication . Preprint . 2006

Quantum spectral curves, quantum integrable systems and the geometric Langlands correspondence

Chervov, A.; Talalaev, D.;
Open Access English
  • Published: 19 Apr 2006
Abstract
The spectral curve is the key ingredient in the modern theory of classical integrable systems. We develop a construction of the ``quantum spectral curve'' and argue that it takes the analogous structural and unifying role on the quantum level also. In the simplest, but essential case the ``quantum spectral curve'' is given by the formula "det"(L(z)-dz) [Talalaev04] (hep-th/0404153). As an easy application of our constructions we obtain the following: quite a universal receipt to define quantum commuting hamiltonians from the classical ones, in particular an explicit description of a maximal commutative subalgebra in U(gl(n)[t])/t^N and in U(\g[t^{-1}])\otimes U(...
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free text keywords: High Energy Physics - Theory, Mathematics - Quantum Algebra, Mathematics - Rings and Algebras
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