The Two-Loop Euler-Heisenberg Lagrangian in Dimensional Renormalization
نویسنده
چکیده
We clarify a discrepancy between two previous calculations of the two-loop QED Euler-Heisenberg Lagrangian, both performed in proper-time regularization, by calculating this quantity in dimensional regularization. e-mail address D.FliegnerThPhys.Uni-Heidelberg.De e-mail address M.G.SchmidtThPhys.Uni-Heidelberg.De e-mail address [email protected] Supported by Deutsche Forschungsgemeinschaft One of the earliest results in quantum electrodynamics was Euler and Heisenberg’s [1] calculation of the one-loop effective Lagrangian induced by an electron loop for an electromagnetic background field with constant field strength tensor Fμν . Written in Schwinger’s proper-time representation [2], this Lagrangian reads L (1) spin[F ] = − 1 8π2 ∫ ∞ 0 dT T 3 e T (eaT )(ebT ) tan(eaT ) tanh(ebT ) . (1) Here a and b may be expressed in terms of the two invariants of the electromagnetic field,
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