The role of wave function in QED

[samalkhaiat]

You need to read about the representation theory of Lorentz group SO(1,3). When you do that, you will see that time is operator (matrix).

I need to be an i***t to be able to make such a super-garbage statement.

Your definition above is correct iff t is c(or r)-number.

Be useful and prove your statement
If you can't then Avoid using "iff" because it would present you as an i***t.

Try to be consistent. If Hans de Vries presentation is a "garbage", then it will remain garbage even if you present it “by TWO very very easy steps”. In addition, try to avoid the NY Times style, since it present you as idiot.

How about Try to understand what you read. I stated the reason for using the word "garbage". So go and do consistency check.

QR, this may be interesting for you: J. Hilgevoord, “Time in quantum mechanics: a story of confusion”

NOT INTERESTED. Maybe the "confusion" part is suitable for you.

regaeds

 

[Hans de Vries]

Mr, samalkhaiatFirst you say that Dirac's equation is capable of treating spin-0 particles:

Haelfix: The Dirac equation treats spin 1/2 particles, but for instance is completely unable to treat spin 0 (Klein-Gordon).

samalhiaiat: This is not true because each component of Dirac spinor does satisfy the K-G equation.

This of course is ignoring:

1) Spin Statistics.
2) The diplole moment interaction terms.

Now when I point out (2), referring to Weinberg (1.1.26)

Dirac also iterated Eq.(1.1.23) obtaining a second-order equation,
which turned out to have just the same form as the Klein-Gordon
equation (1.1.4) except for the presence on the right-hand-side
of two additional terms

\left[ -e\hbar c\ {\vec \sigma}\cdot{\vec B}\ -\ e\hbar c\ {\vec \alpha}\cdot{\vec E} \right]\ \psi \qquad \qquad \mbox{(1.1.26)}

For a slowly moving electron, the first term dominates, and represents
a magnetic moment in agreement with the value (1.1.8) found by
Goudsmit and Uhlenbeck

Then you insult me for a second time without reason by calling this "garbage".

Now for the careful reader of this thread like Anonym this kind of insulting
behavior gives a very strange impression. He told you what this sort of
behavior makes you look like by bluntly using the i-word.

From your response above I do no get the impression that you have
understood this as an appeal to change your behavior and to discuss
in a more civilized manner, unfortunately.Regards, Hans

 

[Anonym]

NOT INTERESTED. Maybe the "confusion" part is suitable for you.

regaeds

QR mean Quantum River. The suggestion adressed to him and related to his post #55 and my answer # 57.

Regaeds.

 

[Anonym]

Now when I point out (2), referring to Weinberg (1.1.26)

In my copy of S.Weinberg it is i also present in the second term which make that operator non self-adjoint. P.A.M. Dirac throw it out without explanation. It seems to me that it is discussed in J.J. Sakurai “Advanced QM” also. What is your comment on it?

 

[Hans de Vries]

In my copy of S.Weinberg it is i also present in the second term which make that operator non self-adjoint. P.A.M. Dirac throw it out without explanation. It seems to me that it is discussed in J.J. Sakurai “Advanced QM” also. What is your comment on it?

The effective Electric moment of the (moving) electron which Dirac
presented in one line with the inherent Magnetic moment in his original
paper seems almost absent in the textbooks.
(See the list I made scanning my books)

Here's Dirac's notation (which uses a comma for the dot product
and the matrix rho which turns the matrix sigma into alpha):

\frac{eh}{c}(\sigma,H) + i\frac{eh}{c}\rho_1(\sigma,E)

Dirac initially dismissed it but it goes straight into QED. It should be right.
A moving electron in an electric field E should have an extra energy term
depending on E since it sees E partly transformed to a magnetic field B
in its rest frame.

Most books don't mention it at all, and if they do, they mostly do so
without discussion. Feynman's book has it and he also gives an alternative
form: (Ninth Lecture)

\left((i\nabla_\mu-eA_\mu)^2\ -\ \frac{i}{2}e\gamma_\mu\gamma_\nu F_{\mu\nu}\right)\Psi\ =\ m^2 \Psi

Which is the twice iterated form of the Dirac equation with the dipole
moments hidden in the F term now. You need to evaluate this term
first before seeing that there is a dependency on the E field and how.

I found this version in Zee (III-6-2)

\left(D_\mu D^\mu - \frac{e}{2}\sigma^{\mu\nu} F_{\mu\nu} +m^2\right)\psi\ =\ 0

I think it is a very basic property and should be discussed in every text
book, and, I think its behavior under rotation and Lorentz transformation
should be discussed. (Which I was planning to study)

Regards, HansThe effective Electric Dipole Moment of the moving electron in the literature:

Aitchison,Hey           Gauge Theories in Particle Physics    No
Berestetskii,Lifshìts   Relativistic Quantum Theory           Yes §32
Bjorken & Drell         Relativistic Quantum Mechanics        No
Chaichian & Nelipa      Intr. to Gauge Field Theories         No
Cottingham & Greenwood  Intr. To the Standard Model           No
Dirac (paper)           The Quantum Theory of the Electron    Yes
Itzykson & Zuber        Quantum Field Theory                  Yes  2-2-3 
Feynman                 Lectures on Physics III               No
Feynman                 Quantum Electrodynamics               Yes 12th lecture 
Feynman                 The Theory of Fundamental Processes   No
Griffits                Intr. to Elementary Particles         No
Halzen & Martin         Quarks & leptons                      No
Heitler                 The Quantum Theory of radiation       No 
Maggiore                A modern introduction to QFT          No
Peskin & Schroeder      Introduction to QFT                   No
Sakurai                 Advanced Quantum Mechaninics          Yes (3.81)
Sakurai                 Modern Quantum Mechanics              No 
Schwinger               Quantum Kinematics and Dynamics       No
Schwinger (editor)      Selected papers on QED                Yes Oppenheimer
Ramond                  Field Theory: A modern Primer         No
Ryder                   Quantum Field Theory                  No
Straeter,Wightman       PCT,Spin,Statistics and all that      No
Strange                 Relativistic Quantum Mechanics        Yes 4.6
Tomonaka,               The story of Spin                     No
Veltman                 Diagrammatica                         No
Weinberg                The Quantum Theory of Fields          Yes (1.1.26)
Zee                     QFT in a nutshell                     (F) (III-6-2)

 

[Anonym]

A moving electron in an electric field E should have an extra energy term depending on E since it sees E partly transformed to a magnetic field B in its rest frame.

-7- Throw away the effective electric dipole moment term.

The latter term is a consequence of the inherent magnetic dipole moment:
An electron moving in a pure E field has an extra energy term because the
E field transforms partly into a B field in the electron's frame. This translates
to an effective electric dipole moment in the rest frame which has an E field
only.

It should be right.

I doubt. What you say, it how it should be (as in classical ED). But H-term is hermitian and E-term is antihermitian. Now here I refer only to P.A.M. Dirac “Principles of QM, 4 Edition, Ch. 11, Par. 70 “Existence of spin”. P.A.M. Dirac do not use the Kronecker (direct) products of underlined Clifford algebra. His presentation mathematically is obscure side by side with the brilliant physical consideration. In addition he is not familiar with C.N. Yang and R.L. Mills paper. If I understand correctly, he obtain Hamilton operator not hermitian in the Schrödinger picture and hermitian in the Heisenberg picture. In addition, if it is the classical ED limit, you expect the electron magnetic moment to be measurable (observable). But N.Bohr said it is not.

I consider this point the main “souvenir” of QED using Vanesch terminology.
I have unfinished business with the coherent states now. I am planning to study next this point also. Thank you very much.

Regards, Dany.

 

[Hans de Vries]

But H-term is hermitian and E-term is antihermitian. Now here I refer only to P.A.M. Dirac “Principles of QM, 4 Edition, Ch. 11, Par. 70 “Existence of spin”.

Indeed,

<br /> \left[-e\hbar c ({\vec \sigma} \cdot {\vec B})\ -\ ie\hbar c \rho_1 <br /> ({\vec \sigma} \cdot {\vec E}) \right] \psi\ \ = \nonumber<br />

<br /> -e\hbar c \left( <br /> \begin{array}{cc|cc}<br /> B_z &amp; B_x-iB_y &amp; iE_z &amp; iE_x+E_y \\<br /> B_x+iB_y &amp; -B_z &amp; iE_x-E_y &amp; -iE_z \\ \hline<br /> iE_z &amp; iE_x+E_y &amp; B_z &amp; B_x-iB_y \\<br /> iE_x-E_y &amp; -iE_z &amp; B_x+iB_y &amp; -B_z <br /> \end{array}<br /> \right)\ \left( <br /> \begin{array}{c}<br /> \psi_1 \\ \psi_2 \\ \psi_3 \\ \psi_4 <br /> \end{array}<br /> \right)<br />But in the standard gamma matrix presentation, which inverts the signs
in the lower half, the entire matrix becomes Hermitian:

<br /> -e\hbar c \left( <br /> \begin{array}{cc|cc}<br /> B_z &amp; B_x-iB_y &amp; iE_z &amp; iE_x+E_y \\<br /> B_x+iB_y &amp; -B_z &amp; iE_x-E_y &amp; -iE_z \\ \hline<br /> -iE_z &amp;-iE_x-E_y &amp; -B_z &amp; -B_x+iB_y \\<br /> -iE_x+E_y &amp; iE_z &amp; -B_x-iB_y &amp; B_z <br /> \end{array}<br /> \right)\ \left( <br /> \begin{array}{c}<br /> \psi_1 \\ \psi_2 \\ \psi_3 \\ \psi_4 <br /> \end{array}<br /> \right)<br />Regards, Hans

 

[Anonym]

I just quoted P.A.M. Dirac. I lost you. I should reproduce your calculations.

Regards, Dany.