Abstract
This paper is an investigation of certain mathematical properties of the vacuum polarization function Σ(s). We show that Σ(s) is a Herglotz function, has no complex zeroes, and belongs to the class of functions called ‘typically real’. In addition, we obtain upper bounds on the higher derivatives of Σ(s), at s=0, given that we know the value of the first derivative at that point.
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Research supported in part by NASA Grant NSG-8035
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Mickens, R.E. Mathematical properties of the vacuum polarization function. Lett Math Phys 2, 343–347 (1978). https://doi.org/10.1007/BF00400158
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DOI: https://doi.org/10.1007/BF00400158