Questions tagged [quantum-electrodynamics]

Quantum electrodynamics (QED) is the quantum field theory believed to describe electromagnetic interaction. It is the simplest example of a quantum gauge theory, where the gauge group is abelian, U(1).

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2answers
246 views

Can we derive the classical beam-splitter theory from the quantum beam-splitter Fock state picture?

A classical beam splitter divides incoming light into two parts according to the reflection and transmission coefficients. A quantum beam splitter on the other hand, can be modelled using Fock states,...
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807 views

Feynman rule for trace over fermion loop

Where does the Feynman rule for "taking the trace over the matrix product arising from a fermion loop" come from? I can not derive it in the "usual way", that is writing the correlator all the way ...
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1answer
374 views

Diagrams involved in 1-loop electron self-energy in QED

I'm following the derivation of electron self-energy at 1-loop in QED on Peskin-Schroeder, page 216. To second order in the coupling the considered diagram (7.15) is The 2-point correlator at second ...
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54 views

Is it possible to derive the correct QED Lagrangian without demanding local gauge invariance?

Usually, the correct interaction term $A_\mu \bar{\Psi} \gamma_\mu \Psi$ in the Lagrangian is derived by demanding local gauge invariance. Is there any other argument that fixes the form of the ...
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1answer
108 views

In charge renormalization equation, $e=e_{0}^{2}\left[1-e_{0}^{2}A\right]$, how can an infinite $e_{0}$ and $A$ give finite $e$ in any limit?

In Griffiths elementary particle book (chapter 7, 'Quantum electrodynamics', equation 7.188), one gets the following equation for the vacuum polarization calculated to one loop correction. $$\frac{e_{...
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Why is the energy of $2s_{1/2}$ greater than the energy of $2p_{1/2}$ after the Lamb shift is taken into account?

The Wikepedia article here defines Lamb shift as a difference in energy between two energy levels $2s_{1/2}$ and $2p_{1/2}$ (in term symbol notation) of the hydrogen atom which was not predicted by ...
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1answer
183 views

The antiparticle of photon is itself

I'm not sure whether this question is redundant, but I think it is probably not due to the focus of the question. We might say that photon does have antiparticle and it is photon it self. I know for ...
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77 views

Interaction of charges [duplicate]

As it is known in Physics, two point-size charges (say two electrons) interact with each other through em forces. How this is happening? do they exchange photons? And if so, then do they exchange ...
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34 views

Does Electromagnetic Inertia has any relation with the emission of Electromagnetic Waves from Accelerated Charged Particles?

We know that Electromagnetic Fields have certain inertia in them. Lenz's Law is a good example to demonstrate Electromagnetic Inertia. Nature resists the change in the state of Electromagnetic Fields ...
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149 views

If electrons are waves, how do they repel each other? [closed]

Louis de Broglie said that electrons are waves. But how they repel each other?
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57 views

Why do the Electric and Magnetic Fields have Different Units?

I just finished my first upper-division E&M course and have a question. Why do the electric field and the magnetic field have different units if they are essentially rotations of each other? ...
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QED vertex correction, proper vertex function and meaning

I might be making great confusion in trying to interpret proper vertex function. I'm studying QED vertex correction. I'm just going to write down the pieces of the puzzle. So I know that the ...
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Diagrams Contributing to Electric Charge Correction (M. Schwartz)

In M. Schwartz's Quantum Field Theory and the Standard Model, he talks about the correction to the $g$-factor in Chapter 17. In Section 17.2 (Pg. 318), he is evaluating the diagram that gives the ...
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155 views

How much electrons can absorb a single photon?

In the one hand, energy can be emitted\absorbed only by a discrete portions. In the other hand - according to Coulomb law the higher distance - the lower force, because count of force lines per area ...
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1answer
37 views

Collapse operators in multi-level atomic systems?

I'm trying to understand the case of multiple ground states and excited states. Due to selection rules, usually we say there should be 3 collapse operators, namely C_+1, C_-1, C_pi, corresponding to ...
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Why are there no loop corrections to the photon mass? [duplicate]

I know that a question about why the photon is massless already exists, however it did not answer this question. First off, I do understand why the photon does neither have a bare mass term due to ...
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92 views

Is the magnetic field energy around a current carrying wire is similar to the electric field energy associated with an isolated charge?

What I mean by this question is, as we say that the electric field energy around a charge is the self energy of the charge, similarly can we say that the magnetic field energy around a current ...
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1answer
55 views

Is the electron field of QED similar to the Higg's field?

If I understand it (I probably don't...) the Higg's field is a field that permeates the universe, and its excitations are the Higg's bosons. It seems that this implies that the Higg's field is a ...
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67 views

Vector Spherical Harmonics and total angular momentum

In their book Akhiezer et al. give a definition of vector spherical harmonics (p.18 of Russian Edition) as $$\pmb{Y}_{j\ell m}(\pmb \Omega) = \sum_{m' \lambda} \langle \ell m' 1\lambda| jm \rangle Y_{...
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1answer
36 views

Wave energy in terms of classical and quantum mechanics [duplicate]

If there are two light waves of same amplitude but of different frequencies then their energy will be same or different? If same then how will you define the light waves as photons and will there be a ...
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1answer
67 views

Double photon emission, half photon absorption

Is it possible for atom with two electons to absorb one photon in this manner, $$|gg\rangle|n\rangle \to |ee\rangle|n-1\rangle$$ or for one electron to emit two photons like this $$|e\rangle|n\...
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63 views

What is interaction cross section of a photon and how to find it?

I encountered this term while reading about photon interaction with metal electrons. Is this equal to the scattering cross section or is it different? How to find it mathematically?
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1answer
66 views

What is the difference between photons in the E-Field and the H-Field?

It is well established that the photon is the propagator for the electromagnetic force. How are the set of photons used in the H-field behaving differently than those in the E-field? Is it different ...
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1answer
319 views

Why can there be only 3-particle vertices in Feynman diagrams? [closed]

Why can there be only 3-particle vertices in Feynman diagrams? For example, when a particle and its anti-particle annihilate to form two photons, why is its Feynmann drawn the way it is in diagram 2 (...
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How does QED explain friction between two bodies?

I was reading Brian Cox's "The Quantum Universe" and at one point he was taking the analogy of the ball resting at the bottom of a valley to explain the finite potential well or "electron in a box" ...
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182 views

Photon creation and quantum field theory

I remember learning the following familiar story in high school chemistry class: "an atom consists of a nucleus of protons and neutrons, and a collection of electrons orbiting around the nucleus ...
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99 views

Don't the magnets slip and turn in Stern-Gerlach experiment, if their orientation is not aligned with the applied magnetic field?

I was watching two videos on YouTube: In this video, there is an attempt to explain what spin is, using analogy of magnets. But here it is shown that magnets which are not aligned with magnetic field ...
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2answers
411 views

Simplify quantum electrodynamics expression

I have a quantum electrodynamics exercise on the one-loop electron self-energy correction in which I need to show that $$ \tag{1} ie^{2}\Sigma(p)=\frac{\left(-ie\right)^{2}}{\left(2\pi\right)^{4}}\...
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256 views

Contact terms in derivation of Ward identity

(This post is a bit long; the key question is between the horizontal lines, and an example follows it.) I am following the derivation of the Ward identity in Schwartz's QFT book, and there is a key ...
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1answer
98 views

Endless electron-positron annihilation/creation?

We start the process with gamma rays collision that produces positron electron pair, the pair then annihilates when hit each other and gamma rays are produced again and everything repeats. Sure, in ...
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How far can we take the analogy of particle exchanges as classical interactions?

In QED, electromagnetic interaction can be thought of as being a result of virtual photon exchanges between charged particles. In some books, it was claimed that to some extent, this interaction can ...
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193 views

How can I do quantum chemistry with QED?

So I am a theoretical and computational chemist by trade and my usual zone of operation in the domain of quantum mechanics is Hartree-Fock and Density Functional Theories. I was thinking if there ...
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185 views

Simplification of an expression with gamma matrices [closed]

I am trying to understand the details of the calculations involved in determining the electron's anomalous magnetic moment to second order: the $\alpha/{2\pi}$ term. There is just one step, where an ...
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121 views

According to Coulomb law, why do fixed charges interact, if they don't emit the photons?

Why does it happens, if fixed charges don't oscillate the em field?
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48 views

Integral representation for inner product in the Gupta-Bleuler quantization

Following the Gupta-Bleuler method for the quantization of the electromagnetic field, we have that: $$[a_{k'\lambda'},\hat{a}^\dagger_{k\lambda}]=-g_{\lambda \lambda'}\delta(k-k')$$ And the vacuum $$\...
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1answer
69 views

Why there is a distance dependence in Coulomb's law if photons can travel to infinity?

Why there is a distance dependence in coulombs law if photons can travel to infinity? Why there is distance dependence at all?
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648 views

What do the arrows on this Feynman diagram represent? [duplicate]

The picture follows the convention of the time axis being on the vertical direction. I think this Feynman diagram represents Coulomb repulsion between two electrons with a virtual photon being ...
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1answer
464 views

Electric dipole moment of electron: about what point is the moment taken?

There is a lot of experimental research activity into whether the electron has an electric dipole moment. The electron, however, has a net charge, and so its dipole moment $$ {\bf \mu}= \int ({\...
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1answer
143 views

Classical Limit of coherent State in Jaynes Cummings Model

Im dealing with an exercise on the Jaynes Cummings model in a resonat single mode approximation. The interaction Hamiltonian in rotating wave approximation is $$H_{int}=g\, \sigma_+\,a\,+g^*\,\sigma_-...
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66 views

Expectation value of the electromagnetic field

According to wikipedia, the operator of the electromagnetic field is given by: $$E \propto \sum_k \sqrt{k}(a_k^{+}e^{-ikr}+a_ke^{ikr})$$ wouldn't that mean that the expactation value of $E^2$ is ...
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1answer
35 views

From a QED perspective, where is an electron on the surface of a charged conducting sphere before it is detected?

Classically, charges on a charged sphere is distributed on the surface as to minimize energy (and distribute like charges as far apart as possible). But in QED a single electrons has a probability ...
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1answer
824 views

Most trivial neutral pion decay

Literature states neutral pion decay by QED cannot occur directly because the pion is uncharged. However, I cannot see why Photons are not allowed to interact with the Quarks directly. Please ...
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1answer
158 views

Acceleration of photon

When light moves from one medium to another its speed changes due to the refractive index of the medium and so does its momentum given by $h/λ$. What is the acceleration of photon when it makes ...
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1answer
177 views

Is there any experimental proof for QED theory? [closed]

Are there any primary experiments used to try to prove the Quantum Electrodynamics theory? Were they all successful, and how were they performed? Also, I was wondering where Feynman's equations are ...
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1answer
54 views

Probability interpretation of electron charge

Consider the QED. When we write the covariant derivative of the theory and couple vector field of gauge boson and the spinor of fermion we think of electric charge of electron $e$ as a coupling ...
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External structure in BPHZ/Hopf algebraic renormalization of QED

I'm currently trying to understand and reproduce the Hopf-algebraic renormalization of QED presented by Walter D. Van Suijlekom. I don't understand why he chooses these external structures in (2), (7),...
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Is QED confining in 2+1 dimensions? Are there experimental realizations in condensed matter systems?

In 1d, QED is confining because the potential is linear and it costs an infinite amount of energy to separate two equal and opposite charges. I am guessing that the same is true in 2d, since the ...
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1answer
45 views

A doubt in Yang-Mills procedure

My question is this: I saw the next relation in a Yang Mills theory paper: $$L_{i}P^{\mu \nu}_{i}=P^{\mu \nu}$$ With $L_{i}$ a generator of su(2) and for any $P^{\mu \nu}_{i}$. But I can't ...
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2answers
99 views

Pair production near an electron

A high energy photon (E>~MeV) after interacting with an atomic nucleus produces an electron positron pair. The threshold of this process is the sum of the rest mass energies of these two leptons. My ...
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70 views

$Z_1=Z_2$ without Ward-Takahashi identity?

In the renormalization of QED, the way that $Z_1=Z_2$ is treated e.g. in Schwartz is by first giving a simple "heuristic argument" based on gauge invariance (in the beginning of section 19.5) before ...