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Introduction:
The Dirac equation
provides a very good description of
physical states of the electron, the muon and of their antiparticles.
These particles carry an electric charge.
Here the electromagnetic interaction takes the form
jμAμ. The Dirac equation
provides a self-consistent expression for the electron's
4-current:
jμ =
e
ψ
γμψ.
This expression satisfies
the continuity equation of Maxwellian electrodynamics
jμ,μ=0.
The Noether theorem is used for a construction of
the Dirac jμ.
These issues which are crucial for every coherent quantum theory of an
electrically charged particle can be found in relevant textbooks.
The W± particles are indispensable elements
of the electroweak theory. Experiments show that
one of the decay modes of the W− consists
of an electron and an antineutrino. It means that the
W− electric charge is identical to
that of the electron.
Question #1:
Why the electroweak theory does not provide a self-consistent
expression for the 4-current
jμ
of the
charge carrying particles W±
together with an adequate proof showing that this 4-current
satisfies the Maxwellian continuity equation and that
it interacts linearly with the electromagnetic 4-potentials
Aμ?
A very strong indication of the lack of such a proof can be inferred from
the fact that, unlike the case of the Dirac equation,
this subject is not discussed in textbooks.
Question #2:
In other fields of physics
primary electromagnetic expressions
have a solid theoretical structure. By contrast, the
CERN's LHC people use an "effective" expression for the calculations of the
electromagnetic interaction of the
W± particles [1]. Why have they
relegated the treatment of the
W± particles
to a phenomenological status?
This is yet another strong indication showing
that the electroweak theory indeed has
no self-consistent expression for the 4-current of the
W± particles.
Question #3:
The electro-weak theory lacks another fundamental
element. Differential equations play a key role in the mathematical structure of
physical theories. Physicists are supposed to know this. On the other hand, one
wonders why textbooks of the electro-weak theory do not explicitly present the
differential equations that describe the particles
W±, which is an indispensable element
of this theory? Moreover, one may wonder - what's going on in the lecture
halls? Can't we find a student who asks what is the differential equation that
describes the time-evolution of the particles W±?
A more detailed discussion of this issue can be found
here.
P.S.
A denial of the assertion of
question #1 is acceptable if and only if one
points out the page numbers of a textbook where a self-consistent
expression for the 4-current of the W±
bosons together with its electromagnetic interaction
is discussed appropriately. The same is true for the differential
equations of the W±.
A telegraphic hint:
The W's Lagrangian density contains a
product of two functions where each of which is a covariant derivative.
Hence, the substitution i∂μ →
i∂μ - eAμ means that
the Noether 4-current
jμ
depends linearly on Aμ.
It follows that the electromagnetic interaction
-jμAμ is
quadratic
in Aμ and in the electric charge e.
This is inconsistent with Maxwellian electrodynamics.
Conclusion: there is no solution for
the electroweak W± contradictions.
References:
[1]
G. Aad et al. (ATLAS Collaboration), Phys. Lett. B712, 289 (2012).
(See eq. (3).)
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