OK thanks, I sent over the calculation of the contact term in our theory, it is much more elegant than the use of the Dirac delta function. As you infer, the vacuum results in a non zero contact term.
To: EMyrone@aol.com
Sent: 15/12/2017 12:08:35 GMT Standard Time
Subj: Re: Discussion of 394(7)The delta function in Maxima is only known as an input function for a Laplace transformation. It cannot be used for general calculations.
Horst
Am 15.12.2017 um 12:58 schrieb EMyrone:
Thanks, this is why the Dirac delta function is needed. Can Maxima derive the result:
del squared (1 / r) = – 4 pi delta sub D (r)
where delta sub D (r) is the Dirac delta function? There are many formulae on the net for the Dirac delta function, and in each formula r can be replaced by r plus delta r
To: EMyrone
Sent: 15/12/2017 11:21:25 GMT Standard Time
Subj: Re: 394(7): Shivering of the Contact TermComputer algebra gives that the contact term vanishes because of
nabla^2 (1/r) = 0.
As can be seen from the protocol, all terms cancel out.
Horst
Am 14.12.2017 um 15:37 schrieb EMyrone:
The contact term in NMR is shown to have a similar structure to that of the magnetic dipole field. This is not apparent from its usual representation as a Dirac delta function, Eq. (2). The effect of the vacuum on the contact field is given by Eq. (17). This seems to be a new insight to the contact field. The vacuum will affect the hyperfine spin spin structure of NMR. There are many ways of representing the Dirac delta function in mathematics, and each method can be corrected for the vacuum shivering. That will lead to a lot of interesting graphics. Dirac’s original idea of a delta function was dismissed outright by mathematicians as complete nonsense, despite its success in physics. The mathematicians later developed theories for the Dirac delta function that showed its deeply insightful nature. As Horst and I have shown in various UFT papers on the Dirac equation, he was not bothered very much about the finer points of mathematics if the physics emerged in a way that made sense. This is OK as far as it goes, but as we have shown, Dirac missed a lot of physics and a lot of people went on missing it for almost a hundred years because they just followed Dirac.