Quantization of Lax integrable systems and Conformal Field Theory

@article{Sheinman2020QuantizationOL,
  title={Quantization of Lax integrable systems and Conformal Field Theory},
  author={Oleg Karlovich Sheinman},
  journal={arXiv: Mathematical Physics},
  year={2020}
}
  • O. Sheinman
  • Published 6 May 2020
  • Mathematics
  • arXiv: Mathematical Physics
We present the correspondence between Lax integrable systems with spectral parameter on a Riemann surface, and Conformal Field Theories, in quite general set-up suggested earlier by the author. This correspondence turns out to give a prequantization of the integrable systems in question. 

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References

SHOWING 1-10 OF 30 REFERENCES

Krichever-Novikov Type Algebras: Theory and Applications

Krichever and Novikov introduced certain classes of infinite dimensional Lie algebras to extend the Virasoro algebra and its related algebras to Riemann surfaces of higher genus. The author of this

Algebras of Virasoro type, Riemann surfaces and strings in Minkowski space

  • Funct. Anal. Appl
  • 1987

Lax Equations and the Knizhnik–Zamolodchikov Connection

Given a Lax system of equations with the spectral parameter on a Riemann surface we construct a projective unitary representation of the Lie algebra of Hamiltonian vector fields by

Current algebras on Riemann surfaces

  • De Gruyter Expositions in Mathematics,
  • 2012

Lax operator algebras and integrable systems

A new class of infinite-dimensional Lie algebras, called Lax operator algebras, is presented, along with a related unifying approach to finite- dimensional integrable systems with a spectral

Hitchin Systems on Hyperelliptic Curves

We describe a class of spectral curves and find explicit formulas for the Darboux coordinates of Hitchin systems corresponding to classical simple groups on hyperelliptic curves. We consider in

Highest Weight Representations Of Infinite Dimensional Lie Algebras

AFFINE KAC-MOODY ALGEBRAS AT THE CRITICAL LEVEL AND GELFAND-DIKII ALGEBRAS

We prove Drinfeld's conjecture that the center of a certain completion of the universal enveloping algebra of an affine Kac-Moody algebra at the critical level is isomorphic to the Gelfand-Dikii

Flat connections and geometric quantization

Using the space of holomorphic symmetric tensors on the moduli space of stable bundles over a Riemann surface we construct a projectively flat connection on a vector bundle over Teichmüller space.