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HIERARCHY OF QUANTUM EXPLICITLY SOLVABLE AND INTEGRABLE MODELS

  • A.K. Pogrebkov
Part of the NATO Science Series book series (NAII, volume 201)

Abstract

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.

Keywords

Integrable Model Classical Limit mKdV Equation Bosonic Operator Linear Evolution Equation 
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Copyright information

© Springer 2006

Authors and Affiliations

  • A.K. Pogrebkov
    • 1
  1. 1.Steklov Mathematical InstituteMoscowRussia

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