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Theoretical and Mathematical Physics

, Volume 129, Issue 2, pp 1586–1595 | Cite as

Quantizing the KdV Equation

  • A. K. Pogrebkov
Article

Abstract

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 of two well-defined operators. Each operator is bilinear and diagonal with respect to either fermion or boson (current) creation/annihilation operators. As a result, the quantization procedure needs no space cutoff and can be performed on the entire axis. In this approach, solitonic states appear in the Hilbert space, and soliton parameters become quantized. We also demonstrate that the dispersionless KdV equation is uniquely and explicitly solvable in the quantum case.

Keywords

Soliton Hilbert Space Quantum Case Quantization Procedure Fermionic Representation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Plenum Publishing Corporation 2001

Authors and Affiliations

  • A. K. Pogrebkov
    • 1
  1. 1.Steklov Mathematical Institute, RASMoscowRussia

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