Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2006-04-19
Physics
High Energy Physics
High Energy Physics - Theory
54 pp. minor changes
Scientific paper
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(t\g[t]); its relation with the center on the of the affine algebra; an explicit formula for the center generators and a conjecture on W-algebra generators; a receipt to obtain the q-deformation of these results; the simple and explicit construction of the Langlands correspondence; the relation between the ``quantum spectral curve'' and the Knizhnik-Zamolodchikov equation; new generalizations of the KZ-equation; the conjecture on rationality of the solutions of the KZ-equation for special values of level. In the simplest cases we observe the coincidence of the ``quantum spectral curve'' and the so-called Baxter equation. Connection with the KZ-equation offers a new powerful way to construct the Baxter's Q-operator.
Chervov Alexander
Talalaev Dmitri
No associations
LandOfFree
Quantum spectral curves, quantum integrable systems and the geometric Langlands correspondence does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Quantum spectral curves, quantum integrable systems and the geometric Langlands correspondence, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Quantum spectral curves, quantum integrable systems and the geometric Langlands correspondence will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-237118