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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