This is one out of several problems with the Dirac approximation, which is H = E = m c squared in the right hand side denominator. This means that the relativistic hamiltonian H = gamma m c squared + U is approximated by H = m c squared, so gamma = 1 and U = 0. The non relativistic hamiltonian H0 = H – m c sqaured is therefore zero, reductio ad absurdum. Despite assuming U = 0, the usual development proceeds with U not equal 0, a diametric self inconsistency. This is how the spin orbit fine structure is obtained, without U there is no spin orbit fine structure at all. Dirac attempted to justify all this in his Nobel lecture by saying that the theory is valid only for slow moving electrons. This never convinced me, and in recent UFT papers this argument by Dirac has been avoided. The development from Eqs. (30) to (32) is the same as the usual theory of the Zeeman effect, in which W is replaced by A, and B = curl A. For a unifomr magnetic field A = (1/2) B x r = (1./2) (curl A) x r. I have not equated curl W with a magnetic field because in the AB vacuum there are no fields, only potentials. In UFT318 the Aharonov Bohm effect was developed briefly with the A potential. Its complete understanding with the W potential needs the complex potential, so
B(1) = curl W(1) – i W(2) x W(3) / W(0)
et cyclicum
so in the Aharonvo Bohm vacuum
W(0) curl W(1) = i W(2) x W(3)
et cyclicum
and B(1) = 0. There are potentials but no fields. I agree with your last point.
In a message dated 21/01/2016 16:35:04 GMT Standard Time writes:
If I see it right, the problem in the Dirac approximation is that in (11) the term H is neglected in the denominator at the RHS, but not in the sum at the LHS. Otherwise we would not obtain an energy operator at all.
I see a problem with the result (32) which is obtained from (30) by using the identity (31). The result (32) does not give a contribution from a cur-free potential W, but eq. (30) does. This seems to be inconsistent. Is there an implicit restriction in eq.(31)? For example that W is rotational in structure exclusively?
Eq.(35) could be inserted into (30) without problems, then it depends only on the scalar productbold p * bold W
or
bold p * bold Omega.Horst
Am 20.01.2016 um 12:34 schrieb EMyrone:
This note begins the development of an entirely new theory of the anomalous g factor of the electron by considering it to be due to the spin connection of the AB vacuum (defined entirely by the spin connection within the quantum of magnetic flux h bar / e). In this first note the conventional g = 2 is derived using the usual Dirac approximation, beginning to look decidedly dippy after the latest UFT papers. In the next note the anomalous g factor of the electron (to any experimental precision) is calculated by removing the Dirac approximation. So the dippy Feynman hocus focus of QED is entirely removed, and a far simpler and more powerful theory emerges and is preferred by Ockham’s Razor. The anomalous g factor is due to the spin connection of the AB vacuum.