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arXiv · hep-th/9503171

Derivatives as an IR Regulator for Massless Fields

Per Elmfors
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Abstract

The free propagator for the scalar $λϕ^4$--theory is calculated exactly up to the second derivative of a background field. Using this propagator I compute the one--loop effective action, which then contains all powers of the field but with at most two derivatives acting on each field. The standard derivative expansion, which only has a finite number of derivatives in each term, breaks down for small fields when the mass is zero, while the expression obtained here has a well--defined expansion in $ϕ$. In this way the resummation of derivatives cures the naive IR divergence. The extension to finite temperature is also discussed.

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Per Elmfors. 1995-03-24. Derivatives as an IR Regulator for Massless Fields. https://doi.org/10.1016/0370-2693(95)00540-2

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