Dispersion Relations and Spectral Representations

  • Wilhelm Brenig


The two response functions Xkl (t) and Φ kl (t) by definition [(2.25) and (3.12)] vanish for t < 0. Physically speaking this expresses “causality”: the “effect” Q(t) is influenced only by “causes” f e(t′) and f(0), at times t′ and 0, respectively, before t. Mathematically one can use this fact to continue the Fourier transform of the correlation functions [e.g. (3.6)] into the (upper) complex ω half plane without endangering the convergence of the Fourier integrals. The Fourier integrals on the real ω-axis then can be obtained as limits of the integrals in the complex plane from above.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.



  1. 6.1
    Kramers, H.A.: Estratto dagli Atti del Congresso Intemazionale di Fisica, Como ( Nicolo Zanichelli, Bologna 1927 )Google Scholar

Additional Reading

  1. Kronig, R. de: Ned. Tijdschr. Natuurkd. 9, 402 (1942); Physica 12, 543 (1946)MathSciNetGoogle Scholar
  2. Kadanoff, LP, Martin, P.C.: Ann. Phys. 24, 419 (1963)MathSciNetADSzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Wilhelm Brenig
    • 1
  1. 1.Physik-DepartmentTechnische Universität MünchenGarchingFed. Rep. of Germany

Personalised recommendations