Re: Pfadintegral verstanden (Zee)

[Supersede/Fortsetzung]

Hendrik van Hees schrieb:

Inge Bein wrote:

Woher hast du denn diese Auffassung? Hast du das Buch schon gelesen?

Ja.

Welche Auffassung hältst du für eine "Enttäuschung"?

Es sind nicht die Auffassungen, sondern die oberflächliche Darstellung.

Das ist nicht oberflächlich, im Gegenteil, diese Methode führt
zu Verständnis, nicht zu 'shut'n calc' - Biomaschinen, Beispiel:

"
1.5. Coulomb and Newton: Repulsion and Attraction

....
Comparing with E) and using the well-known fact that 1 + 1 - 2/3) > 0,
we see that while like charges repel, masses attract. Trumpets, please!


The universe

It is difficult to overstate the importance (not to speak of the beauty)
of what we have learned: The exchange of a spin 0 particle produces an
attractive force, of a spin 1 particle a repulsive force, and of a
spin 2 particle an attractive force, realized in the hadronic strong
interaction, the electromagnetic interaction, and the gravitational
interaction, respectively. The universal attraction of gravity produces
an instability that drives the formation of structure in the early
universe. Denser regions become denser yet. The attractive nuclear
force mediated by the spin 0 particle eventually ignites the stars.
Furthermore, the attractive force between protons and neutrons mediated
by the spin 0 particle is able to overcome the repulsive electric force
between protons mediated by the spin 1 particle to form a variety of
nuclei without which the world would certainly be rather boring. The
repulsion between likes and hence attraction between opposites generated
by the spin 1 particle allow electrically neutral atoms to form.
The world results from a subtle interplay among spin 0, 1, and 2.
In this lightning tour of the universe, we did not mention the weak
interaction. In fact, the weak interaction plays a crucial role in
keeping stars such as our sun burning at a steady rate. "

Wenn du von "einer der größten Enttäuschungen" sprichst, dann sag
dazu, daß *du* enttäuscht bist, und sprich nicht für die ganze Welt.

Direkt weiter im Buch:

"
Degrees of freedom

Now for a bit of cold water: Logically and mathematically the physics
of a particle with mass m != 0 could well be different from the physics
with m = 0. Indeed, we know from classical electromagnetism that an
electromagnetic wave has 2 polarizations, that is, 2 degrees of freedom.
For a massive spin 1 particle we can go to its rest frame, where the
rotation group tells us that there are 2*1 + 1 = 3 degrees of freedom.

The crucial piece of physics is that we can never bring the massless
photon to its rest frame.

Mathematically, the rotation group SO(3) degenerates into SO(2),
the group of 2-dimensional rotations around the direction of
the photon's momentum.

We will see in Chapter II.7 that the longitudinal degree of freedom
of a massive spin 1 meson decouples as we take the mass to zero. The
treatment given here for the interaction between charges (6) is correct.
However, in the case of gravity, the 2/3 in 17) is replaced by 1 in
Einstein's theory, as we will see Chapter VIII.l. Fortunately, the sign
of the interaction given in 17) does not change. Mute the trumpets a bit.


I. Motivation and Foundation

Appendix
Pretend that we never heard of the Maxwell Lagrangian. We want to
construct a relativistic Lagrangian for a massive spin 1 meson field.
Together we will discover Maxwell. Spin 1 means that the field
transforms as a vector under the 3-dimensional rotation group. The
simplest Lorentz object that contains the 3-dimensional vector is
obviously the 4- ..."
.

Relevant Pages

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