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. 
View PDF on arXiv
3 Citations
Background Citations
1
Methods Citations
2

3 Citations

Gromov–Witten invariants of target curves via Symplectic Field Theory

$$ T\overline{T} $$-deformation and long range spin chains

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 $$…

T (cid:22) T -deformation and long range spin chains

,

References

SHOWING 1-10 OF 25 REFERENCES

Integrable structure of conformal field theory, quantum KdV theory and Thermodynamic Bethe Ansatz

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…

Do anyons solve Heisenberg's Urgleichung in one dimension

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…

The dispersionless Lax equations and topological minimal models

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…

Solitons : differential equations, symmetries and infinite dimensional algebras

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…

Quantum Inverse Scattering Method and Correlation Functions

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…

INTEGRABILITY OF THE QUANTUM KdV EQUATION AT c=−2

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.

Quantizing the KdV Equation

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…

Associativity equations in dispersionless integrable hierarchies

Temperature correlation functions in the XX0 Heisenberg chain. I

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

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.…