QFT Interpretation of Electron and Attached EM Field

In summary, Schwinger's calculation of g-2 to leading order was done without considering the electron, while higher-order corrections to the photon field polarization are still important for phenomena like spectroscopy.
  • #1
CSnowden
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This is an elementary question on visualizing the interaction of an electron with the surrounding EM field in QFT. I believe in QFT the electron is viewed as an excitation of the Electron matter field with an associated coupling constant between the electron field and EM field (say q) - q 'couples' the two fields and allows the electron to feel a force from the local value of the extended (free) EM field. But in classical physics many electrons together would be said to generate a higher surrounding EM field value, presumably by the combination of the attached EM field each generates. In QFT does the q coupling from each electron also raise the local EM field value, in addition to allowing the the electron (electron field excitation) to 'feel' the force from the EM field.
 
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  • #2
CSnowden said:
In QFT does the q coupling from each electron also raise the local EM field value, in addition to allowing the the electron (electron field excitation) to 'feel' the force from the EM field.
Yes. Each electron is accompanied by an electromagnetic field, which is additive and approximately of Coulomb form.
 
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  • #3
That's very helpful, thanks. Just to clarify, in the use of the term 'attached EM field of an electron' does this refer to a elevation of the energy level of the local EM field neighboring the electron, ie. is there truly just one pervasive EM field and not separate 'attached' fields in addition. Are the electron and EM quantum field equations asymmetrical in some respect so that electron field quantum (local field excitation) couples to raise the local EM field energy level but the reverse does not happen (ie. an EM quantum like a photon does not raise the energy level of the surrounding electron field)? Or perhaps this is intrinsic to the nature of the fields themselves, with one a field of spinor values and the other a field of vector values?
 
  • #4
If I understand your question correctly, the answer is that there is symmetry - just as the interaction causes a change in the local properties of electrons, the interaction also causes a change in the local property of photons. For example, if [itex]g=0[/itex], photons will never interact - they simply pass through each other. In contrast, the simple fact that [itex]g\neq 0[/itex] means that actually two photons will scatter off of each other, even if there is no electron (excitation of the electron field) in the universe.

In an interacting QFT, the general rule is that everything affects everything; it is a true many-body problem. For example, there is no coupling constant between the electron and the muon, but since they both couple to the photon, the existence of one has an effect on the other. (Since the electron is lighter, is has a larger effect on the muon than vice-versa.)
 
  • #5
king vitamin said:
Since the electron is lighter, is has a larger effect on the muon than vice-versa.
No, just the opposite. Since the electron is lighter, is has a smaller effect on the muon than vice-versa.
CSnowden said:
is there truly just one pervasive EM field and not separate 'attached' fields in addition.
There is just one electromagnetic field, just as in classical mechanics there is only one Hamiltonian. But the electromagnetic field can be decomposed into a sum of pieces coming from different sources and the remainder, just as a Hamiltonian can be decomposed into a sum of energy contributions from each particle in the noninteracting case, and particle pairs, triples, etc., in case of interactions.
 
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  • #6
Thanks to all, this has been very helpful!
 
  • #7
A. Neumaier said:
No, just the opposite. Since the electron is lighter, is has a smaller effect on the muon than vice-versa.

It would be a horrible thing if physics worked this way. We would need to know about all of the most massive particles (up to the Planck scale and beyond) in order to calculate the properties of the electron!

But it's not true. Schwinger only needed to consider the electron to compute g-2 to leading order, and contributions due to muon/tauon loops are much smaller (though still needed to match the extraordinary experimental precision we have). Similarly, since the electron strongly dominates over (for example) the leading correction to the photon field polarization, it dominates over certain higher-order contributions of g-2 of the muon compared to similar loops with virtual muons and tauons. (What I mean is that removing the electron field from the theory would have a bigger effect on the muon's g-2 than the corresponding thought experiment of the effect of removing the muon to the electron's g-2.) This is because propagators come with factors of the mass of the particle in the denominator, so heavier particles always contribute less in perturbation theory (and I think one can use RG arguments to make this statement nonperturbative, though this isn't needed for QED).

In fact, this is why the discrepancies in the muon's g-2 (compared to the electron) are considered predictors for more massive particles somewhere beyond the Standard Model. Corrections to this physical value due to some unobserved more massive particle with mass [itex]m_X[/itex] scale like [itex]m_{\mu}/m_{X}[/itex], so it makes sense to see the discrepancy in the more massive muon rather than the electron where this correction is smaller. (For a reference, see for example the first section of this review article: https://arxiv.org/abs/hep-ph/0703125v3).
 
  • #8
king vitamin said:
Schwinger only needed to consider the electron to compute g-2 to leading order, and contributions due to muon/tauon loops are much smaller
Ah, your statements are about virtual processes involving the electron and the muon, where indeed the most massive particles have the least influence.
But mine was about real electrons or muons, and a real muon affects the dynamics much more than a real electron.
 

1. What is QFT Interpretation of Electron and Attached EM Field?

QFT (Quantum Field Theory) is a theoretical framework used to describe the behavior of subatomic particles, including electrons. The QFT interpretation of electrons states that they are not point-like particles, but rather excitations of a quantum field that permeates all of space. The attached EM (electromagnetic) field is a fundamental force that is carried by particles called photons and is responsible for interactions between charged particles.

2. How does QFT explain the behavior of electrons?

In QFT, electrons are described as excitations of a quantum field, which is a mathematical concept that represents the possible states of a particle. This means that the behavior of electrons can be understood as fluctuations in this field. The attached EM field plays a crucial role in this behavior, as it can interact with the electron and cause it to move or change states.

3. What is the relationship between QFT and the Standard Model?

The Standard Model is a theory that describes the fundamental particles and forces of nature. QFT is a mathematical framework that is used to describe the behavior of these particles and how they interact with each other. In the Standard Model, the electron is described as a point-like particle, but QFT provides a more detailed understanding of its behavior as an excitation of a quantum field.

4. Can QFT explain the wave-particle duality of electrons?

Yes, QFT can explain the wave-particle duality of electrons. In this interpretation, electrons are both particles and waves, and their behavior can be described by a wave function that gives the probability of finding the electron at a specific location. This wave function is a manifestation of the underlying quantum field and can change depending on the interactions with the attached EM field.

5. How does QFT interpretation of electrons impact our understanding of the universe?

The QFT interpretation of electrons and the attached EM field provides a deeper understanding of the subatomic world and how particles interact with each other. It has also led to the development of many important theories and technologies, such as the Standard Model and quantum computing. This interpretation has also helped scientists make significant advancements in fields such as cosmology, particle physics, and quantum mechanics, leading to a more comprehensive understanding of the universe.

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