Maclaurin series expansion of the Vacuum Correction

This is given by the general formula (5). Its use in quantum physics is exemplified by the accurate calculation of the Lamb shift. The vacuum corrections to the Newtonian and Coulombic potentials are worked out with well known expressions for the Dirac delta function, Eqs. (19) and (20). Mean square fluctuations in the vacuum can be worked out classically using the statistical mechanics of vacuum particles and Monte Carlo and molecular dynamics methods. This method can be used for any scalar function of relevance in physics. The Maclaurin expansion was inferred by Colin Maclaurin, who became a full professor of mathematics at Marechal College Aberdeen at the age of 19.


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