# HIERARCHY OF QUANTUM EXPLICITLY SOLVABLE AND INTEGRABLE MODELS

@article{Pogrebkov2002HIERARCHYOQ,
title={HIERARCHY OF QUANTUM EXPLICITLY SOLVABLE AND INTEGRABLE MODELS},
author={Andrei K. Pogrebkov},
journal={arXiv: Exactly Solvable and Integrable Systems},
year={2002},
pages={231-244}
}
• A. Pogrebkov
• Published 20 February 2002
• Physics
• arXiv: Exactly Solvable and Integrable Systems
Realizing bosonic field v(x) as current of massless (chiral) fermions we derive hierarchy of quantum polynomial interactions of the field v(x) that are completely integrable and lead to linear evolutions for the fermionic field. It is proved that in the classical limit this hierarchy reduces to the dispersionless KdV hierarchy. Application of our construction to quantization of generic completely integrable interaction is demonstrated by example of the mKdV equation.
3 Citations
• Physics
Journal of High Energy Physics
• 2020
Abstract We point out that two classes of deformations of integrable models, developed completely independently, have deep connections and share the same algebraic origin. One class includes the 

## References

SHOWING 1-10 OF 25 REFERENCES

• Mathematics
• 1996
AbstractWe construct the quantum versions of the monodromy matrices of KdV theory. The traces of these quantum monodromy matrices, which will be called as “T-operators,” act in highest weight
• Physics
• 1998
Abstract. We construct solutions to the chiral Thirring model in the framework of algebraic quantum field theory. We find that for all positive temperatures there are fermionic solutions only if the
It is shown that perturbed rings of the primary chiral fields of the topological minimal models coincide with some particular solutions of the dispersionless Lax equations. The exact formulae for the
Preface 1. The KdV equation and its symmetries 2. The KdV hierarchy 3. The Hirota equation and vertex operators 4. The calculus of Fermions 5. The Boson-Fermion correspondence 6. Transformation
• Physics, Mathematics
• 1993
One-dimensional Bose-gas One-dimensional Heisenberg magnet Massive Thirring model Classical r-matrix Fundamentals of inverse scattering method Algebraic Bethe ansatz Quantum field theory integral
• Physics
• 1991
We present a simple direct proof of the complete integrability of the quantum KdV equation at c=−2, with an explicit description of all the conservation laws.
We consider the quantization procedure for the Gardner–Zakharov–Faddeev and Magri brackets using the fermionic representation for the KdV field. In both cases, the corresponding Hamiltonians are sums
• Mathematics
• 1993
Space and time dependent correlation functions in the Heisenberg XX0 chain (in the transverse magnetic field) are expressed in terms of Fredholm determinants of linear integral operators. This is
A geometrical approach to the nonlinear solvable equations, based on the study of the “groups of motion” of special infinite-dimensional manifolds called “symplectic Kahler manifolds”, is suggested.