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Relations between classical phase-space distributions and Wigner function for multiparticle production processes

The effects of interpreting classical phase space distributions as Wigner functions, which is common in models of multiparticle production, are discussed. The temperature for the classical description is always higher than that for its Wigner function interpretation. A rough estimate shows that the corresponding correction is proportional to R^(-2), where R is the radius of the interaction region, and that it is negligible for heavy ion scattering, but at the few percent level for e^+e^- annihilations.