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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Why is it important that the vector current should be conserved in QED?

In Quantum Field Theory and the Standard Model by MD Schwartz in the chapter about the anomalies, he derives from the equation of motions and the Noether currents of a effective massless QED ...
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Can a light be bent by a magnetic field?

I'm struck with two competing ideas on the question in the title. Listing #1: http://van.physics.illinois.edu/qa/listing.php?id=2009 Q: "How far can a magnetic field bend light?" A: "Unfortunately, ...
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Virtual photon counting

How to calculate number of exchanged virtual photons per unit of time between two electromagnetically interacting objects?
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Time ordering, interaction Lagrangian calculation, QED

I am trying to compute $$ \langle 0| \, T\left\{\phi^\dagger(x_1) \phi(x_2) \exp \left[i \! \int{L_1(x) \, \mathrm{d}x} \right] \right\}|0 \rangle $$ for $$ L_1(x) = ...
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Charge dependence of operators in QED renormalization

Consider a UV cutoff regulator $\Lambda$ with an effective QED lagrangian: $\mathcal{L}_{\Lambda} = \bar{\psi}_{\Lambda}(i\not \partial - m_{\Lambda})\psi_{\Lambda} - ...
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What are the “two surfaces” in QED's reflection by two surfaces

When Feynman refers to the "top surface" and "bottom surface" probabilities when explaining QED, is he referring to the probability of the photons reaching the top of the object and the bottom of the ...
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Electric field due to rotating charged sphere

Consider a spherically symmetric charged object (charge $Q$) rotating about its axis. From Gauss's law we know that all that matters for the electric field $\mathbf{E}$ is the charge $Q$ enclosed ...
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Differential cross section for photon scattering on fixed magnetic dipole

Photon with energy $\hbar\omega$ scattering on a fixed particle with magnetic momentum $\vec{\mu} = \mu \vec s$. How to calculate a differential and total cross section for the photon. I've found in ...
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How is charge expressed?

I am happy with the concept of electrons interacting with each other through the emission and absorption of photons, but what I don't understand is how the negative charge on an electron is expressed ...
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How do two electrical charged particles know to repel or attract each other?

Now per QED, electrical charges interactions are effected by photons. Suppose you are one of the two charges. How do you know to attract or repel the other charge? In other words, how do you know if ...
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QED: what is the relationship between emission and absorbtion spectrums? (and why do plants absorb blue light and emit green light..)

I'm interested in this because of photosynthesis, but hte question is general. I'm looking for a QED explanation. A lot of the explanations talk about light shining on a plant getting aborbed, ...
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Intuition behind $U(1)$-gauge model of Electrodynamics in a general spacetime

As the article Electrodynamics in general spacetime greatly explains, the $U(1)$-gauge theory is a good base for working in non-simply connected spaces. But I wonder whether there is a deep reason to ...
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Non-minimal coupling (Pauli Coupling) of gauge field with a non-relativistic scalar field

I am wondering if it makes any sense to non-minimally (say, Pauli-like) couple an external gauge field with a non-relativistic scalar field: \begin{equation} p_\mu \rightarrow p_\mu - e A_\mu + ...
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Why doesn't a changed particle ever lose energy by interacting with others by radiation of virtual photons? Are all virtual photons exchanged?

I've had it explained to me in a separate post that charged particles are constantly exchanging virtual particles with other charged particles and their energy is a steady state. How it is a surety ...
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Can a quark irreversibly pass though an event horizon?

This is an attempt to transform a question I asked about a year ago into a binary yes-or-no question: Since a quark has electrical charge, can it irreversibly pass though an event horizon? The ...
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Photo-excitation in terms of particle physics [duplicate]

How does a photon couple to an electron during an excitation/de-excitation process in an atom? My current understanding is rather limited especially when considering types of fundamental forces and ...
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Why the extra term $\frac{1}{2}(\partial_{\rho}A^{\rho})^2$ in the photon Lagrangian?

In my quantum field theory class we have been told to use this Lagrangian for the photon field $$\mathcal{L}=-\frac{1}{4}F_{\alpha\beta}F^{\alpha\beta} -\frac{1}{2}(\partial_{\rho}A^{\rho})^2.$$ but ...
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Can the granular quantum nature of light be used to engineer a maroscopic optical phenomena?

Today we have optical metamaterials and metasurfaces: materials and surfaces that are made of unit cells with an approximate size of tens of nanometers, that can that interact with light and can have ...
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Admixtures of longitudinal and timelike photons!

In the quantization of electromagnetic field the physical states $|\psi\rangle$ are found to obey the following relation: $[a^{(0)}(k)-a^{(3)}(k)]|\psi\rangle=0$ It is explained as the physical ...
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Which renormalisation techniques are available for 3+1 QED?

I hope my question is not too naive, but I would like to know what are the available renormalisation techniques for 3+1 QED. I have read a bit about Pauli-Villars, but I am wondering if there are ...
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Commutation of field and atomic ladder operators in the Dicke model

Consider the Dicke model, whose Hamiltonian is (in the rotating wave approximation) \begin{equation} \hat H=\omega_c \hat a^\dagger \hat a+\omega_0 \hat \sigma_z + g(\hat a^\dagger \hat \sigma + \hat ...
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How is 2D spectroscopy able to show quantum coherent transport through networks?

For wave-like (quantum coherent) energy transfer in networks (eg. propagation of excitation in photosynthetic protein complexes of algae or FMO complex in plants) 2D electronic (photon echo?) ...
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How positron and electron annihilate forming photons? [duplicate]

Electron is a particle with momentum $p$ and it spins up. Positron is its antiparticle having momentum $-p$ and it spins down. "A positron is an electron travelling backwards in time" said by Feynman. ...
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What is $Q_p/Q_e$ experimentally? [duplicate]

What is the experimental value of the ratio between the proton and the electron charge? Or more generally, is there a table that lists the ratio of the different nuclei charges to that of the ...
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One loop correction to $F^2$ in massless QED, question from Peskin & Schroeder

In Peskin & Schroeder chapter 19, about trace anomaly in massless QED, the trace of $\Theta^{\mu\nu}$ is given by $$ {\Theta^\mu} _\mu =-\frac{4-d}{4} (F_{\lambda\sigma})^2 + (1-d) \bar{\psi} i ...
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Can we find the definite path of electron?

Light can crisscross in all directions. Source: Can photons pass through each other? In a given volume, we can have light throughout, such that there is no space with no light in it (with the ...
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Help to understand vertex function

In Weinberg's book (the quantum theory of fields, volume 1, pag 446, equation (10.4.19) ) is stated that $\int \ dx \ dy \ dz \ exp(-i p x - ik y + i lz) \langle\Psi_0,T\{J^{\mu}(x)\Psi_n(y)\bar ...
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Electron's self-energy in QED in arbitrary gauge

Recently I've tried to evaluate electron's self-energy in QED in the second order of perturbation theory by using dimensional regularization. Corresponding 1PI-diagram leads to $$ \Sigma_{1loop} = ...
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Are all positrons electrons traveling back in time?

I have recently read Richard Feynman's "QED" and in it Feynman describes positrons as 'how we view electrons when they are going back in time and we are stuck traveling forwards in time'. I was ...
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Regularization of infrared divergences

Let's have diagrams in QED when we don't use Feynman gauge. Then the bare photon propagator will look like $$ \tag 1 D_{\mu \nu}(p) = -\frac{g_{\mu \nu} - \frac{p_{\mu}p_{\nu}}{p^{2}}}{p^{2} + ...
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Radiative mass generation in QED?

Does self-energy correction leading to a modification in the mass of the electron can be called radiative mass generation? In Zee model of radiative neutrino mass generation, the helicity of the ...
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Convergence of light by light scattering amplitude

Perhaps I'm too exhausted to see the answer of why the photon-photon scattering should contain no divergences. In Peskin and Schroeder page 320 we find that because of the Ward identity the ...
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Heisenberg approach of Quantum Electrodynamics

I am reading the book of Gunar Kallen "Quantum Electrodynamics" and in the Chapter VI he study the Vacuum polarization. He computes the experimental observable current ...
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Fermion propagator decomposition

I've seen the following decomposition for the fermion propagator for a fermion with momenta $p-k$, and where both $p-k$ and $p$ have a mass of $m$: $$\frac{(\not p-\not k)+m}{(p-k)^2-m^2}\gamma_\mu= ...
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Gauge choice after Spontaneous Symmetry Breaking

After the spontaneous breakdown of local symmetry in presence of gauge fields (Higgs Mechanism), we can always choose a gauge where the Goldstone bosons are eaten up by the gauge field (also called ...
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QED Vertex Factor/Rule

On page 303 in Peskin&Schroeder they give the vertex factor as $$V = -ie\gamma^\mu \int d^4x$$ while on page 304 they write $$V_\times = -ie\gamma^\mu\int d^4x A_\mu(x).$$ Why are the ...
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In QED, why is the $e^- + e^+\leftrightarrow\gamma$ process forbidden on-shell?

QED has a vertex that couples a single photon to two fermions. This vertex describes the annihilation of an electron-positron pair into a photon. Why is this process forbidden for all three particles ...
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Integration & bremsstrahlung calculation

In this paper (relevant pdf section) that I'm reading, involving the calculation of bremsstrahlung in electron proton scattering (diagram below), the author calculates the integral over outgoing ...
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Deriving the Coulomb force equation from the idea of photon exchange?

Since Newton's law of gravitation can be gotten out of Einstein's field equatons as an approximation, I was wondering whether the same applies for the electromagnetic force being the exchange of ...
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Non-invariance of the Interaction term in QED lagrangian

The interaction term in the QED Lagrangian $$\mathcal{L}_{int}=e\bar\psi\gamma^\mu A_\mu\psi$$ changes under a gauge transformation $$A_\mu\rightarrow A_\mu+\partial_\mu\chi$$ Doesn’t it affect the ...
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Feynman propagator with general $\xi$ parameter

Hey from my notes in my PS book it seems I have solved this some time in the past, but I cannot seem to get the indices straight this time around. So in deriving the Feynman photon-propagator which ...
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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 ...
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Ward identity derived from global symmetry and SDE, different from that derived from gauge symmetry?

In QED, according to Schwinger-Dyson equation $^{[1]}$, $$\left(\eta^{\mu\nu}(\partial ^2)-(1-\frac{1}{\xi})\partial^{\mu}\partial^{\nu}\right)\langle 0|\mathcal{T}A_{\nu}(x)...|0\rangle = e\,\langle ...
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Can the diffraction/interference pattern behind the slit (double slit) be calculated with Feynman path integrals (QED)?

I often see Feynman path integrals explained by a graphic which shows the slit and then the electron goes all possible ways behind the slit. Ok that is nice to understand the Feynman path integral, ...
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Spinor normalizations in Breit-frame: electric and magnetic form factors

We usually have the normalization (see e.g. page 110 in Halzen & Martin "Quarks and Leptons") $$u^{(r)\dagger}u^{(s)} = 2E\delta_{rs}$$ which leads to $${\bar{u}^{(s)}}u^{(s)} = 2m. $$ ...
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Is the QED description of an electron/photon complete?

Is it possible that a future theory would add more information and understanding about electrons, photons etc., or is QED the best we can do?
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Connection between Gauge Fixing Term and Gauge Condition [duplicate]

In Peskin on page 514, when deriving the Faddeev-Poppov ghosts, they arrive at the full Lagrangian for Yang-Mills: $$ \mathcal{L} = -\frac{1}{4}F^2 + \frac{1}{2\xi} (\partial \cdot ...
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A step in the derivation of the magnetic moment of the electron in Zee's QFT book

In chapter III.6 of his Quantum Field Theory in a Nutshell, A. Zee sets out to derive the magnetic moment of an electron in quantum electrodynamics. He starts by replacing in the Dirac equation the ...
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Hamiltonian split into Mass term and Decay Width

I have encountered the following procedure several times now, and none of the sources ever explain the physical reason behind it: The Hamiltonian $H$ is split into $M$ and $\Gamma$. WHY? Where ...
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how is an electron able to emit and absorb the same (virtual) photon?

When calculating the lowest order self energy corrections for an electron for example, feynman diagrams involving the emission and re-absorption of a (virtual) photon need to be considered, (as here ...