What are space-like and time-like virtual photons?

[Frame Dragger]

The operators (propagators) always use the invariant mass of the particle.
The off-the-shell "masses" are not really masses. The virtual particles are
always interactions between the fermion field and the electromagnetic field.
The two different types of field always propagate with their own invariant
mass.

Is this not equivalent to saying that virtual particles are a mathematical trick to describe/calculate those interactions within Perturbation Theory!?

 

[tiny-tim]

Hi Hans!

… ok then … what is the physical understanding of an internal electron line in an EM Feynman diagram?

The internal electron line is most easily thought of as the propagation from the interaction between the incoming electron and photon. Starting from the interactive Dirac equation …
…
We can isolate the interaction term at the left hand side.
…
The propagator for the internal electron is the inverse of the operator on the
right hand site. The operator's Fourier transform in the momentum domain is.
…
and so the inverse operator is …

That's the mathematical process that the line represents.

A Feynman diagram is just a diagram. It, and any line in it, does no more than represent a mathematical process. And that mathematical process may or may not represent a physical process.

I'm asking, what is the physical understanding of an internal electron line?

d'Alembertian operator: …

In momentum space this operator is q^2 and its inverse operator is 1/q^2

The operators (propagators) always use the invariant mass of the particle.
The off-the-shell "masses" are not really masses. The virtual particles are
always interactions between the fermion field and the electromagnetic field.
The two different types of field always propagate with their own invariant
mass.

I'm really asking whether it's the same d'Alembertian operator (in coordinate space).

Differential operators as a way of getting to Feynman diagrams are completely foreign to me.

I'm just asking whether there are two d'Alembertian operators, d'A_e for an electron, and d'A_φ for a photon, or is there just one operator, d'A ?

 

[Hans de Vries]

The operators (propagators) always use the invariant mass of the particle.
The off-the-shell "masses" are not really masses. The virtual particles are
always interactions between the fermion field and the electromagnetic field.
The two different types of field always propagate with their own invariant
mass.

Is this not equivalent to saying that virtual particles are a mathematical trick to describe/calculate those interactions within Perturbation Theory!?

I would says that it shows that using the term "virtual particle" is a bad
and confusing habbit. I do it, and everybody does it but it doesn't
behave as such.

A "space-like virtual particle" would propagate with an imaginary mass
and FTL. In reality there is (in QED) only the massless photon propagator
and the lepton propagator its invariant mass.


Regards, Hans

 

[Frame Dragger]

I would says that it shows that using the term "virtual particle" is a bad
and confusing habbit. I do it, and everybody does it but it doesn't
behave as such.

A "space-like virtual particle" would propagate with an imaginary mass
and FTL. In reality there is (in QED) only the massless photon propagator
and the lepton propagator its invariant mass.


Regards, Hans

I agree that a better term should be used, and in general I think the lexicon of SR/GR/QM needs to be revised and codified. That said, it seems that you're agreeing with me, which would disagree with your previous position and therefore agreeing with Tiny-Tim. I'm confused.

 

[Hans de Vries]

Hi Hans!

That's the mathematical process that the line represents.

A Feynman diagram is just a diagram. It, and any line in it, does no more than represent a mathematical process. And that mathematical process may or may not represent a physical process.

I'm asking, what is the physical understanding of an internal electron line?


I'm really asking whether it's the same d'Alembertian operator (in coordinate space).

Differential operators as a way of getting to Feynman diagrams are completely foreign to me.

I'm just asking whether there are two d'Alembertian operators, d'A_e for an electron, and d'A_φ for a photon, or is there just one operator, d'A ?

Hi, Tiny Tim

The Dirac algebra describes real physics, Just like the equations of the electromagnetic
field, and the mathematical symbol handling in Feynman diagrams can be understood
in terms of real physics, or at least in geometrical terms with vectors, axial vectors
and so on. But indeed, the textbooks usually don't get beyond the purely abstract
mathematical symbol handling, which is really sad.
To gain understanding one can to do the following.

-Start with the observables.
These are things which can be visualized: The charge/ current density, the axial
current density, the magnetization/polarization tensor.- Gain an understanding what propagators are in position space,
how the mass less 1/q propagator spreads a signal on the light cone, and how other
propagators can always be derived from (interacting) mass less propagators.-Study how the Weyl bispinor consist out of two interacting Chiral components
(the mass less left and right handed chiral components. How the direction of each
component is both a momentum direction and a spin direction, one with a left handed
chiralty and one with a right handed chiralty.-Understand what the pauli matrices do geometrically,
and what the i does geometrically:

Multiplying by -i\sigma^i rotates the spinor by 180^o around the x^i-axis
Multiplying by i rotates the spinor by -180^o around its own axis

This means that a multiplication of an x-up-spinor by the pauli-x-matrix is rotated
by 0 degrees while the same multiplication rotates an x-down-spinor by 360 degrees,
(which amounts to a multiplication by -1). This provides us with a way to obtain
the x-component of the spin vector of the spinor. The spin-vector is consequently
given by:

<br /> \vec{(\xi)} ~=~<br /> \left(\begin{array}{c}<br /> \xi^*\sigma^x\xi \\ \xi^*\sigma^y\xi \\ \xi^*\sigma^z\xi<br /> \end{array}\right)<br />

This vector represents both a current as well as a spin direction. It means that we
can express the total vector-current, as well as the total axial current, with the
mass-less spin vectors as:

<br /> \begin{array}{ll}<br /> \mbox{vector current:} ~~ &amp; =~~ +\vec{(\xi)}_R - \vec{(\xi)}_L \\<br /> \mbox{axial current:} ~~ &amp; =~~ -\vec{(\xi)}_R - \vec{(\xi)}_L \\<br /> \end{array}<br />

So, now we have already derived these two basic observables in a geometrical
way which we can visualize with pictures representing the underlying physics.Regards, Hans

 

[tiny-tim]

Hi Hans!

Yes, I understand all of that.

(though I don't see what propagators in position space have to do with virtual particles which can only exist in momentum space )

But i don't understand, and you're still not answering, …

what is the physical understanding of an internal electron line? ​

 

[Hans de Vries]

Hi Hans!

Yes, I understand all of that.

(though I don't see what propagators in position space have to do with virtual particles which can only exist in momentum space )

But i don't understand, and you're still not answering, …

what is the physical understanding of an internal electron line? ​

It's an electron propagating under the influence of an electromagnetic field.

An internal electron line originates from the original electron but has a changed
momentum so that the interference charge/current density between the two
generates an electromagnetic field which negates (absorbs) the em field of the
incoming photon.

Regards, Hans

 

[Frame Dragger]

It's an electron propagating under the influence of an electromagnetic field.

An internal electron line originates from the original electron but has a changed
momentum so that the interference charge/current density between the two
generates an electromagnetic field which negates (absorbs) the em field of the
incoming photon.

Regards, Hans

That happens, but that's not a virtual photon.

 

[tiny-tim]

virtual electrons?

Everything in the Feynman diagrams can be physically understood. It is just a question of working it out mathematically.

… ok then … what is the physical understanding of an internal electron line in an EM Feynman diagram?

It's an electron propagating under the influence of an electromagnetic field.

An internal electron line originates from the original electron but has a changed momentum so that the interference charge/current density between the two generates an electromagnetic field which negates (absorbs) the em field of the incoming photon.

(Do you mean "an internal electron originates from the original electron but has a changed momentum {etc}"?)

I don't understand the physical meaning of "originates from the original electron".

"originates" how? where? and how/where does it de-originate?

And are you saying then that there is a physical internal electron for each internal electron line in each Feynman diagram (of which of course there are infinitely many) for the particular process?

And are you saying that there is a separate physical interference charge/current density between the original electron and each separate internal electron? And is there similarly a physical interference charge/current density between each pair of internal electrons?

Finally, what "incoming photon" (whose em field is to be negated)?

I didn't specify either an incoming or an outgoing photon in the interaction, and there doesn't have to be one!​

 

[Hans de Vries]

That happens, but that's not a virtual photon.

They call it a "virtual electron" instead...

 

[Hans de Vries]

(Do you mean "an internal electron originates from the original electron but has a changed momentum {etc}"?)

Yes

I don't understand the physical meaning of "originates from the original electron".

"originates" how? where? and how/where does it de-originate?

It is the original electron field pertubated by the (alternating) photon field.
You have to think about the interaction of planewaves. The scattering zone
is considered wide enough to make this assumption valid.

And are you saying then that there is a physical internal electron for each internal electron line in each Feynman diagram (of which of course there are infinitely many) for the particular process?

In higher order diagrams there are electron and positron fields. Again, calling something
an electron and basing this on one of the quantization methods (electrons as
quantized excitations of the electron field) is something what you can do, or not do,
but it is not relevant for the end result. The pertubative series development is valid
with or without this interpretation of the individual terms.

And are you saying that there is a separate physical interference charge/current density between the original electron and each separate internal electron? And is there similarly a physical interference charge/current density between each pair of internal electrons?

No. The interaction is only with the photon which is connected to the interaction vertex.

Finally, what "incoming photon" (whose em field is to be negated)?

I didn't specify either an incoming or an outgoing photon in the interaction, and there doesn't have to be one!​

There has to be a photon, either incoming, outgoing or internal (if you are restricting
this to QED).


Regards, Hans

 

[Frame Dragger]

They call it a "virtual electron" instead...

I don't see how that helps in any way.

 

[Hans de Vries]

I don't see how that helps in any way.

Are you agreeing or objecting? Because I gave some reasons against
calling them "virtual particles" or worse, "space-like virtual particles"

Vacuum polarization could be associated with "virtual particles" if you
like, as long as the off-the-shell behavior is interpreted as the result
from interaction rather than from a propagator with an off-the-shell
mass.

Regards, Hans

 

[Frame Dragger]

Are you agreeing or objecting? Because I gave some reasons against
calling them "virtual particles" or worse, "space-like virtual particles"

Vacuum polarization could be associated with "virtual particles" if you
like, as long as the off-the-shell behavior is interpreted as the result
from interaction rather than from a propagator with an off-the-shell
mass.

Regards, Hans

I disagree with your definition of a virtual photon, but I agree that the term can be misleading... just not for the reasons you seem to think.

 

[Hans de Vries]

I disagree with your definition of a virtual photon, but I agree that the term can be misleading... just not for the reasons you seem to think.

I don't have a definition of what a "virtual photon" is...

-I have a definition of what goes on in a feynman diagram with an internal photon.
-I have a definition of what does not exist: virtual photons with a space-like imaginary mass.

Can you be more specific?

Regards, Hans

 

[Frame Dragger]

I don't have a definition of what a "virtual photon" is...

-I have a definition of what goes on in a feynman diagram with an internal photon.
-I have a definition of what does not exist: virtual photons with a space-like imaginary mass.

Can you be more specific?

Regards, Hans

I don't mean this as any kind of insult, but page 5 is too late to restart this discussion from basic principles. I think we're ultimately talking about the same physical (and transitional non-physical) processess, but we're not communicating that well. I think at this point You, myself, and Tiny-Tim are unlikely to change our views when they seem to be so entrenched. That, or against all odds, you're completely wrong, and I don't feel qualified or confident enough to show that. Tiny-Tim and you seem to be a better match; I'm no physicist, just a duffer.

 

[tupos]

An internal electron line originates from the original electron but has a changed
momentum

Regards, Hans

Nonsense. The definition of real electron

p^2 = -m_{R}^2 where m_{R} is a real experimental mass.

There is no evidence to conclude that p^2 is equal to m^2 for internal electron line.

The same with photon, no evidence to say that k^2 = 0 for internal photon line.


Regards.

 

[Hans de Vries]

Nonsense. The definition of real electron

p^2 = -m_{R}^2 where m_{R} is a real experimental mass.

There is no evidence to conclude that p^2 is equal to m^2 for internal electron line.

The same with photon, no evidence to say that k^2 = 0 for internal photon line.Regards.

Read my posts before shouting. Where did I ever make these statements which you
call nonsense? On the contrary, I'm protesting against descriptions which implicitly
make such assumptions, such as: "space-like virtual photons"

 

[tupos]

Hello Hans,

I didn't shout. Sorry if you get me wrong, I agree with you that there is no sense in space like and so on.

But you wrote and I commented it that "An internal electron line originates from the original electron but has a changed
momentum" you wrote it. I agree that nonsense is too strong word for this, maybe slightly incorrect is better

 

[Hans de Vries]

Hello Hans,

I didn't shout. Sorry if you get me wrong, I agree with you that there is no sense in space like and so on.

Hi, Tupos It's fine thank you.

But you wrote and I commented it that "An internal electron line originates from the original electron but has a changed
momentum" you wrote it. I agree that nonsense is too strong word for this, maybe slightly incorrect is better

Maybe that's a too popular description for you? A more technical description was given
here in this post: https://www.physicsforums.com/showpost.php?p=2574073&postcount=60

Regards, Hans

 

[tupos]

I know very well what is internal electron line. I just wanted to point out your attention that internal electron line is not a real electron because for this virtual particle it is not necessary that p=-m^2, that's all.