Agreed, since this is a quantum mechanical calculation, an expectation value is needed, denoted by the angular brackets. The Taylor series does not use the Dirac delta function, whereas the usual Lamb shift calculation uses the Dirac delta function.
Coulomb Potential and Tensor Taylor Series
To: Myron Evans <myronevans123>
In eq.(18) it is shown that the Taylor series should give the same result as mode theory for <Delta phi>. Mode theory gives a constant expression for <delta r * delta r>. The Taylor expression of Delta phi has to be integrated to give the expectation value <Delta phi> , at least this is my interpretation of the angle bracket. This means integration of the terms from the Taylor series.
Horst
Am 03.01.2018 um 12:32 schrieb Myron Evans:
The idea in this note is to use the tensor Taylor series to reproduce the experimental value of the Lamb shift as in Eq. (18) and to find the vacuum fluctuations needed to give the Lamb shift. This is done on the classical level without use of the Dirac delta function.