Quantum-ElectroDynamics (QED) is the quantum field theory believed to describe the electromagnetic interaction (and with some extension the weak nuclear force).

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What low-level process drives a frequency-doubling crystal?

I was reading about second-harmonic generation (SHG) crystals (or frequency-doubling crystals) used to produce green laser light from IR. What low-level process in the crystal is actually driving ...
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Did the Goudsmit-Uhlenbeck analysis of spin consider relativity?

It's frequently mentioned in introductory quantum mechanics texts that Goudsmit and Uhlenbeck conjectured that the magnetic moment of an electron was due to angular momentum arising from the electron ...
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Coulomb interaction as virtual particles exchange?

I've been reading about virtual particle exchanges in physics books and in Physics SA posts, where a particle interpretation of gravity and Coulomb interaction is established. The Feynman Diagram ...
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What is predicted to happen for electron beams in the Stern-Gerlach experiment?

The Stern–Gerlach experiment has been carried out for silver and hydrogen atoms, with the result that the beams are deflected discretely rather than continuously by an inhomogenous magnetic field. ...
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How could we describe the electric bound state like hydrogen by QED? [duplicate]

We can solve the Schrodinger equation for the Hamiltonian operator from the classical Hamiltonian of hydrogen bound state, consisting of proton and electron attracting each other electrodynamically, ...
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317 views

Polarization Sums in QCD for the calculation of parton model splitting functions

Before i state the actual problem, here's a premise. In the case of a Spin 1 massive particle it's possible to demonstrate that $$\sum_{\lambda=0,\pm1}\epsilon_{\lambda}^{* \ \mu}\epsilon_{\lambda}^{\...
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In the context of quantum field theory, what does it mean to “couple” something?

Suppose I have the following Lagrangian density \begin{equation} \mathcal{L} = - \frac{1}{4} F_{\mu\nu}F^{\mu\nu} \end{equation} The lecture notes I an reading suggest if I want to "couple to matter",...
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Vacuum polarization of dark matter candidates

Can a dark matter particle (axions, for instance, but the question applies to any valid candidate for dark matter) induce QED vacuum polarization effects even if being electrically neutral and with no ...
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Revisiting the microscopic concept of Touching with some more questions

This question is regarding the amazing answer given by Terry Bollinger at this Phys.SE post. I think this answer is very helpful but i do have some standing questions. He says Once the bonding ...
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On-shellness of photons

In principle, we could describe all physics without EM fields (or photons), as they are mainly a useful tool to describe "action at distance" (which does not mean instantaneous) between charged ...
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How to get Hamiltonian of QED from lagrangian?

I have the QED lagrangian: $$ L = \bar {\Psi}(i \gamma^{\mu }\partial_{\mu} + q\gamma^{\mu}A_{\mu} - m)\Psi + \frac{1}{16 \pi}F_{\alpha \beta}F^{\alpha \beta} . $$ I tried to get hamiltonian by ...
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How to derive the form of the parity operator acting on Lorentz spinors?

I'm reading Berestetskii (Volume 4 of Landau & Lifshitz) section 19 on inversion of spinors. Berestetskii says parity $P$ maps undotted spinors into dotted spinors and vice-versa as $\xi^{A}\...
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Stability of a rotating ring of multiple electrons at relativistic speeds

There was a time when physicists where concerned about electron internal structure. The rotating ring model was one of the proposals to explain how a charge density could become stable against ...
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Measuring the Dirac field

If the Dirac field $\psi(x)$ is to the electron as the Electromagnetic field is to the photon, why is it that we can measure the Electromagnetic field, whereas the Dirac field we cannot?
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How are bound states handled in QFT?

QFT seems very well suited to handle scattering amplitudes between particles represented by the fields in the Lagrangian. But what if you want to know something about a bound state without including ...
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Instantaneous Coulomb interaction in QED

It seems I am stuck with a (at a first sight) trivial problem. It's from the "Quarks and Leptons" (Halzen, Martin) book page $141$, where one considers the following integral: $$\tag{1} T_{fi} = -...
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What physics does occur at short distances in QED?

Let us take the standard QED ($e^-, e^+, \gamma$) as a model of QFT and ask what is its "short-distance" physics? They say the UV infinities appear because we do not know the real physics of short ...
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Under which representation of U(1) transform electron and photon gauge field?

I know that under $SU(2) \times SU(2)$, the left-handed electron transforms under $ ( \frac{1}{2},0 ) $ representation and the vector gauge field $A_\mu$ under $ ( \frac{1}{2},\frac{1}{2}) $. Since ...
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Why/how does an electron emit a photon when decelerating?

I've had two special relativity courses so far but none really gave me a clear description of the process.
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What is the value of the fine structure constant at Planck energy?

At low energy, 511 keV, the value of the fine structure constant is 1/137.03599... At Planck energy $\sqrt{\frac{\hbar c^5}{G}}$, or 1.956 $\times$ 109 Joule, or 1.22 $\times$ 1028 eV, it has a ...
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Width of a photon. And its length

Everyone is always talking about photon's wavelength. But what about its dimensions? What is length and width of it? And does it even have a point to think about such things? Or those dimensions are ...
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Spacelike and timelike photons

I know the definition of space-like and time-like intervals. How do you show that in some reaction the virtual photon(s) is spacelike/timelike? On page 191 Peskin and Schroeder, it says "since $q^2&...
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Feynman diagram for attractive forces

I’m looking at Feynman diagrams for attractive forces and I'm thoroughly confused. Below are three diagrams from HyperPhysics: These all illustrate instances where the forces are attractive. ...
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481 views

What does the magnetic field of the (quantum-mechanical) electron look like?

While a treatment of electron spin can be found in any introductory textbook, I've noticed that the electron's magnetic field seems to be treated classically. Presumably this is because a quantum ...
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What is the density of virtual photons around a unit charge?

It seems that virtual photons also exist in vacuum. So the precise question is: What is the additional virtual photon density due to the electric field of a unit charge? Or: How many virtual photons ...
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Which elementary particles are behind magnetic field, similar as photons behind radio waves?

I see, there are photons behind radio waves. As Wave–particle duality said: the radio waves are waves and at the same time are fluxes of particles called Photons. I'm wondering, what is behind ...
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Propagation speed of photons when taking higher-order QFT corrections into account

In our group of experimental physicist who have nothing to do with and know very little about quantum field theory, we recently had a question concerning the propagation speed of photons in vacuum: ...
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Photon as the carrier of the electromagnetic force

My physics background goes as "far" as reading popsci books on QM, Particle Physics, and Cosmology so pardon my ignorance in the below questions. I've read that the photon is the particle (quanta in ...
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How do we visualise antenna reception of individua radiowave photons building up to a resonant AC current on the antenna?

I am a chemical/biological scientist by trade and wish to understand how quantum EM phenomena translates to our more recognizable classical world. In particular I want to get a mechanistic picture of ...
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Validity of the 'photon wavetrain' model of coherence

In some optics textbooks, coherence is introduced with the "photon wavetrain" model. In this model, we consider light generated by many atoms each making the same transition. During each transition, a ...
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Two questions about Feynman propagator

Taking for example the meson propagator: $$ \Delta_F (x-y) = \int \frac{d^4k}{(2\pi)^4} \frac{e^{-ik(x-y)}}{k^2 - m^2 + i\epsilon}. $$ It describes a meson that propagate from a point of Minkowski ...
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How does a photon “know” that it's left one charge and that it's going to another one?

How does it know the same charge it left will be the same charge it will return to? My understanding is photons are neutral and have no charge. i.e. Like charges repel, unlike attract. All charged ...
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Massless $\lambda \phi^4$ QFT

The $\lambda \phi^4$ quantum filed theory is the textbook example (which probably cannot be constructed nonperturbatively; I'm purely interested in perturbation theory). However, usually one treats ...
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Mass dimension of coupling constants in various dimensions

Just a quick question: Suppose I want to consider QED or YM in 4 dimensions we always say that the coupling constants are dimensionless and that the field then has a specific mass dimension. What ...
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Negative mass dirac equation -> Propagator?

There are two types of dirac equations: $(p_\mu\gamma^\mu - m)\Psi(x) = 0$ and $(p_\mu\gamma^\mu + m)\Psi(x) = 0$. Here $p$ are the momentum operators. The fermion propagator is defined in the ...
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proof of radius of convergence of perturbation series in quantum electrodynamics zero

Can anyone show detailed proof of why radius of convergence of perturbation series in quantum electrodynamics is zero? And how is perturbation series constructed? So, as this argument requires ...
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Is wave–particle duality considered a valid interpretation of the behavior of photons?

There are a number of questions on this site that explain the many wave-like behaviors of photons by making reference to wave-particle duality. However, I have just finished reading Feynman's book ...
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Snell's law starting from QED? [duplicate]

Can one "interpret" Snell's law in terms of QED and the photon picture? How would one justifiy this interpretation with some degree of mathematical rigour? At the end I would like to have a direct ...
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Proton is made of 3 quarks of each spin 1/2, but the total spin of proton also 1/2, how it is possible?

Proton is made of 3 quarks (UUD) each has a spin of 1/2, so if you follow the constitution the total spin of the proton must be (3/2), but the spin of the proton is still 1/2. How it is possible? But ...
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How to count the number of modes/polarizations of a Gaussian field theory?

A Gaussian (free) field theory is described by a quadratic action of the field, e.g. $S=\int\psi^\dagger K\psi$ (or $S=\frac{1}{2}\int\phi^\intercal K\phi$ for real fields). Usually one just need to ...
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How does determinism manifest out of QFT?

Classical electrodynamics is deterministic. QED is indeterministic, or probabilistically random. Yet they agree with each other? What am I missing?
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Characteristic of photons for constant speed

What characteristic of photons causes them to travel with constant speed in all frames of reference? Till the topics I have studied, we always assume this but never got any ideas what can be in the ...
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Is there any relationship between Gravity and Electromagnetism? [duplicate]

We all know that the universe is governed by four Fundamental Forces which are The strong force , The weak force , The electromagnetic force and The gravitational force . Now, is there any ...
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Can the Biot-Savart law be derived from QED?

It's important that a new theory of physics contains the equations and results of previous related ones. Maxwell theory and QED both have explanations for electromagnetic phenomena so I'm wondering if ...
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Doubt in Dyson's argument about the divergent nature of the perturbative expansion in QED

I am trying to understand Dyson's argument about the divergent nature of the perturbative expansion in QED. Quoting his own words [...] let $$F(e^2)=a_0+a_1e^2+a_2e^4+\ldots$$ be a physical ...
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If a photon doesn't necessarily travel in a straight line, doesn't it defy the law of cons. of momentum?

I just finished reading Richard Feynman's lectures on Quantum Electrodynamics (QED: The Strange Theory of Light and Matter) and it fascinated me. However, there's an unanswered question I have from ...
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How does the electric field operator change inside an optical cavity

In the free field, transverse electric field operator is given by the below expression; $$d^{\bot}(R)=i \sum_{p,\lambda}\Big( \frac{\hbar cq}{2V\epsilon_{0}}\Big)^{1/2} \{e^{(\lambda)}(p)a^{(\lambda)}...
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Scattering amplitude with on-shell virtual photon

Let's assume electron-electron scattering in QED in second order of perturbation theory. Then in the corresponding scattering amplitude there will appear photon propagator $$ D_{\mu \nu}(q = p_{i} - ...
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Feynman graph of induced current

I'm self studying QFT from Peskin and Schroeder. In chapter 19 of this book, page 653 (Perturbation theory anomalies) the expectation value of the induced current is calculated. I'm confused with the ...
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Tadpole diagram in QED

In $\phi^4$ theory with the $\lambda \phi^4 / 4!$ interaction term gives rise to “tadpole” diagrams like this: If I have a standard QED interaction with $e \bar\psi \gamma^\mu \psi A_\mu$, can I ...