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Momentum eigenvalue equation for interacting systems

  • J. T. Anderson
Article

Summary

An eigenvalue equation for the excitation momenta of an interacting system is obtained in first-order perturbation theory from self-consistent equations of motion for the particles and the field. The result is a form of the Cauchy-Riemann equations and provides a necessary condition for analyticity on the momentum plane.

Keywords

Interact System Quantum Plasma Scalar Wave Equation Density Matrix Form Vertex Part 
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.

--Уравнение собственных эначений импульса для вэаимодействуюших систем

Реэюме

В первом порядке теории воэмушений иэ самосогласованных уравнений движения для частиц и поля выводится уравнение собственных эначений для импульса воэбуждения вэаимодействуюших систем. Реэультат представлен в форме уравнений Кощи-Римана и обеспечивает необходимое условие для аналитичности в плоскости импульса.

Riassunto

Si ottiene un’equazione agli autovalori per gli impulsi di eccitazione di un sistema interagente, nel primo ordine della teoria delle perturbazioni, in base alle equazioni autoconsistenti del moto per le particelle ed il campo. Il risultato è una forma di equazioni di Cauchy-Riemann e fornisce una condizione necessaria per l’analiticità nel piano degli impulsi.

References

  1. (1).
    J. T. Anderson:Journ. Math. Phys. (in press).Google Scholar
  2. (2).
    J. J. Quinn andS. Rodriguez:Phys. Rev.,128, 2494 (1962).ADSCrossRefGoogle Scholar
  3. (3).
    V. B. Bonch-Bruevich andS. V. Tyablikov:The Green’s Function Method in Statistical Mechanics, Chapt. 7 (Amsterdam, 1962).Google Scholar
  4. (4).
    An introduction to the extensive literature in the use of the density matrix equation in statistical mechanics isP. Résibois:Physica,29, 721 (1964), which also includes a list of additional references.CrossRefGoogle Scholar

Copyright information

© Società Italiana di Fisica 1967

Authors and Affiliations

  • J. T. Anderson
    • 1
  1. 1.Naval Ordnance LaboratoryCorona

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