Symmetry Properties of Correlation Functions

  • Wilhelm Brenig


In this chapter we are going to derive three symmetry relations of the correlation functions that follow either directly from their definition or from the invariance of nature under translations or reversal of time. There are further symmetry properties that follow from the invariance of nature under translations in space, Galilean invariance and possible symmetry properties of the equilibrium state (homogeneity and isotropy of liquids and gases or lattice symmetry of solids), which we will consider only in examples later on.


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  1. 7.1
    For information about time reversal invariance see monographs on quantum mechanics, e.g. Gottfried, K.: Quantum Mechanics I (Benjamin, New York 1966) Chap. 39Google Scholar
  2. 7.2
    Wigner, E.P.: Göttinger Nachr. 31, 546 (1932)Google Scholar

Additional Reading

  1. Forster, D.: Hydrodynamic Fluctuations, Broken Symmetry, and Correlation Functions (W.A. Benjamin, Reading, MA 1975) Sect. 3.2Google Scholar
  2. Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II, Springer Ser. Solid-State Sci., Vol.31 (Springer, Berlin, Heidelberg 1985) Sect. 4.3Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

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

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