S Matrix and Low Energy Theorem in the Theory of Correlation Functions

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Abstract
We have examined the current correlation functions is statistical mechanics from a scattering theory viewpoint. In the light of low energy theorems, we study the connection between the long wavelength, low-frequency correlation functions of conserved currents and the on-shell scattering matrix elements which describe the collision processes taking place in the thermodynamical system of interest. Explicit general formulas are derived for the leading correction terms to the ideal gas correlation functions. These correction terms include the effect of two-body scatterings and double scatterings in three-body events. They are expressed in terms of two-body cross section, time delay, and the quantum analog of the distance of closest approach. Their connection to the second virial coefficient is established through sum rules. Relationship between our results and the Boltzmann equation is discussed.