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S. Weinberg,
the Nobel laureate for his contributions to the electroweak
theory, states in his well known textbook:
First, some good news: quantum
field theory is based on the same quantum mechanics that was invented by
Schroedinger, Heisenberg, Pauli, Born, and others in 1925-26, and has
been used ever since in atomic, molecular, nuclear and condensed matter
physics.
(See [1]. A relevant discussion can be found in [2]). This statement
means that a quantum field theory of an
elementary particle must be consistent with quantum mechanical requirements.
It is well known that the Hilbert space is an important
quantum mechanical attribute
of an elementary particle (see e.g. item (i) of [1]).
This space is built on the basis of a consistent expression for a
function that describes density. (The 3-dimensional integral of density
is unity, which means that the quantum particle exists somewhere in
space.) Furthermore, the Fock space is based on the Hilbert space
(see
here
.)
However, the Z particle of the electroweak theory and the
ordinary Higgs particle (these particles are elements of the Standard
Model) have no valid expressions for density
(and the Noether theorem does not work for these particles). Therefore, the
presently accepted theories of these particles have neither a Hilbert
space nor a Fock space.
Conclusion: The Standard Model contains fundamental errors.
To refute this far reaching conclusion one should merely point out
an explicit and self-consistent
expression for density which is written in
a textbook. If the above mentioned conclusion is wrong then this should
have been an easy task, since the Higgs idea and the electroweak theory
are about half a century old, and they are extensively discussed in
appropriate textbooks.
BTW. In contrast, it is interesting to point out that
the status of well established
physical theories is completely different. For example,
particle density is consistently defined in every (or
very nearly every) textbook on either the Schroedinger equation or
the Dirac equation.
This comparison of the Dirac theory of the electron with the
Standard Model theory of the Z and the Higgs particles
illuminates the ill structure of the Standard Model.
References:
[1] S. Weinberg, The Quantum Theory of Fields,
Vol. I (Cambridge University Press, Cambridge, 1995). (See p. 49
here
.)
[2] F. Rohrlich, Classical Charged Particles,
(World Scientific, New Jersey, 2007).
(see pp. 1-6
here
.)
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