|
|
1. Introduction
The following discussion relies on well established physical concepts
that have been published in (quite old) textbooks and articles.
In spite of their relevance to the understanding of particle physics,
these concepts are apparently
unknown to too many current researchers that work in this field.
This state of affairs has prevented the construction of correct
theories. This is one reason that explains why
the Standard Model contains erroneous elements.
The validity of these statements is shown below.
2. Inherent Isospin Properties
Spin and isospin are based on the same SU(2) group.
In the case of spin, the raising and lowering operators
J± = Jx ±
iJy
play an important role. For a given
eigenfunction of an irreducible multiplet of
J2, the operators
J± have the following important properties:
they only raise/lower the M eigenvalue of the function whereas all
other eigenvalues are unaltered
(see e.g. [1], pp. 78-88, [2], pp. 141-147, [3], Chapter III).
As stated above, spin and isospin are based on the
same mathematical group. Hence, one finds that isospin properties
are analogous to those of spin (see [4], pp. 27-30, [5], pp. 183-191,
[6], pp. 357,358).
In particular, apart from a normalization factor,
isospin raising/lowering operators only replace
a neutron by a proton or vice versa.
In particular, all members of an isospin multiplet have the same
space-spin structure.
In particle physics isospin
symmetry also applies to the u, d quarks.
Conclusion #1:
Let us examine the
four Δ(1232) baryons: Δ-, Δ0,
Δ+, Δ++ which are an isospin quartet.
Therefore, all of them have the same space-spin state. Now,
Δ+ is an excited state of the proton. Hence,
its three valence quarks are not single particle
spatial ground state s-wave.
An application of the raising/lowering isospin operators
proves that also the Δ++,
Δ- baryons are not
single particle ground state s-wave.
The same argument also applies to the Ω- baryon.
Conclusion #2:
QCD has been constructed on the basis of an erroneous argument. A
short explanation of this claim together with an adequate
amount of references is presented
here
.
For reading a full article, click
here
.
3. The Multi-configuration Structure of Quantum States
All physicists agree to points 1 and 2.
-
A closed system has a well defined angular momentum.
-
If the state of a closed system is determined by strong or electromagnetic
interactions then that system has a well defined parity.
These requirements are used in a construction of an atomic state of
more than one electron. Thus, the solution of the problem
can be written as
a linear combination of configurations where each of which has
the same parity and the single particle angular momentum
of the electrons are coupled
in a form that agrees with the total angular momentum of the state.
This issue has already been recognized in the early days of quantum mechanics
(see [3], section XV, [7]).
This procedure is called Configuration Interaction and its
solution yields the Hamiltonian's eigenvalues and
its eigenfunctions.
The significance of this method has been confirmed in the early
days of the electronic computer era [8].
The calculations prove that even a quite simple state like the
0+ ground
state of the helium atom is described by many configurations and
that no single configuration plays a dominant role.
There is a well-known approximation called the "Central
Field Approximation", where each electron is assumed to move in a
spherically symmetric potential that represents the nuclear potential
and the potential of all other electrons (see [2], p. 277). In this
approximation, the state of a muti-electron atom takes the form
of a single configuration. The results shown in the
previous paragraph prove the following conclusion.
Conclusion #3:
The Central Field Approximation is far away from reality.
It turns out that the entire particle physics community has overlooked
this important conclusion. This state of affairs is the reason
for the "Proton Spin Crisis". This "crisis" is still regarded as an
unsolved problem (see
here
).
For reading a full article that explains this issue and
settles the crisis, click
here
.
4. Concluding Remarks
The contents of sections 2,3 substantiate the claim of section 1 which
says that the current community of particle physicists
apparently does not know fundamental issues that are relevant to their field.
This fact provides an explanation for specific Standard Model errors.
Several examples of this matter are shown
here
.
References:
[1] L. D. Landau and E. M. Lifshitz, Quantun Mechanics
(Pergamon, London, 1959).
[2] L. I. Schiff, Quantum Mechanics (McGraw-Hill, New York, 1955).
[3] E. U. Condon and G. H. Shortly,
The Theory of Atomic Spectra (Cambrige, University Press, 1935).
[4] S. S. M. Wong, Introductory Nuclear Physics (Wiley, New York, 1998).
[5] A. de-Shalit and I. Talmi, Nuclear Shell Theory (Academic,
New York, 1963).
[6] D. H. Perkins, Introduction to high energy physics (Addison,
Menlo Park, 1987).
[7] G. R. Taylor and R. G. Parr, Superposition of configurations:
The helium atom, Proc., Natl. Acad. Sci. USA 38, 154 (1952).
[8] A. W. Weiss, Phys. Rev. 122, 1826 (1961).
|
|
|
