Model solutions of regularized relativistic transport equations

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Abstract
We present numerical solutions of recently proposed relativistic transport equations for fluctuating hadronic fields with simplified model Lagrangians containing a spin-1/2 nucleon and a light scalar or pseudoscalar meson. We introduce and implement a method for regularizing tadpoles and vector loops which is consistent with the previously proposed regularization of the scalar loops. The resulting solutions in vacuum are well behaved, exhibiting the expected differences between the scalar and pseudoscalar cases without apparent pathologies.

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