Il Nuovo Cimento A (1965-1970)

, Volume 2, Issue 3, pp 632–640 | Cite as

On the quantization of an essentially nonlinear field

  • D. I. Blohinčev


An essentially nonlinear field implies here a field obeying a certain equation with characteristics depending on the field itself or its derivatives. The simplest example of quantization of an essentially nonlinear system with one degree of freedom is first considered. Then a method of quantization of the essentially nonlinear field of the type of the Born-Infeld field is described.


Un campo essenzialmente non lineare implica un campo che obbedisce ad una equazione con caratteristiche dipendenti dal campo stesso o dalle sue derivate. Si considera dapprima l’esempio più semplice di quantizzazione di un sistema essenzialmente non lineare con un grado di libertà. Successivamente si descrive un metodo di quantizzazione del campo essenzialmente non lineare del tipo del campo di Born-Infeld.


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  1. (*).
    See paper (1). Note that, for the sake of simplicity, we write down the Lagrangian (1) for a two-dimensional world.MATHCrossRefADSGoogle Scholar
  2. (1).
    M. Born:Proc. Roy. Soc., A143, 410 (1934).CrossRefADSGoogle Scholar
  3. (*).
    Earlier I called this spectral state «the fusion of events» (see papers (2,3)).Google Scholar
  4. (2).
    D. Blohinčev:Dokl. Akad. Nauk SSSR,32, 553 (1952).Google Scholar
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  8. (*).
    The connection of the essentially nonlinear theory with the metrics was already noted in ref. (2) and was described in more detail in ref. (6,7).Google Scholar
  9. (6).
    D. I. Blohinčev:Dokl. Akad. Nauk SSSR,168, 774 (1966).Google Scholar
  10. (7).
    Dao Vong Duk andNguen Van Cheu: preprint P2-4605 (Dubna, 1969).Google Scholar
  11. (*).
    This consideration is also supported by the results of ref. (4), where it is shown that the success in solving an essentially nonlinear problem is based on the transition from the Cartesian co-ordinate system (x, t) to the curvilinear one (α, β) the axes of which coincide with the directions of the characteristic curves.Google Scholar
  12. (8).
    R. Feiman andA. Hibs:Quantum Mechanics and Integrals (Moscow, 1968).Google Scholar

Copyright information

© Società Italiana di Fisica 1971

Authors and Affiliations

  • D. I. Blohinčev
    • 1
  1. 1.Joint Institute for Nuclear ResearchDubna (Moscow)

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