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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Is it possible to give photons an electric charge?

I know that photons have no electric charge and that they are stable, but is it possible to give them a positive or negative charge? If so how?
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Integral calculation [on hold]

I do some calculation in QED, but I can not calculate such integral $$ I(a_1,a_2,m_1,m_2)=\int\frac{ d^2\mathbf{x} d^2\mathbf{y}}{(1+\mathbf{x}^2)(1+\mathbf{y}^2)((\mathbf{x}+a_1 ...
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Is there an expression for field charge analogous to field mass?

In electrodynamics, it is possible to derive an expression for the field momentum for a given moving charge distribution (e.g. a sphere with uniform velocity) and from that infer an "electromagnetic ...
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Could future experiments on “Gravitational Casimir Effect” confirm the existence of gravitons?

From Casimir effect, we know that when two plates are placed very close to each other in vacuum, they attract each other because the quantum fluctuations that press on the two plates' outer surfaces ...
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Is the elementary charge really a constant of nature? - Accuracy of QED

There are a couple of natural constants; examples are Planck's constant or the Speed of light in vacuum. The elementary Charge is the coupling factor to all Kind of electromagnetic interactions; this ...
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Are electron fields and photon fields part of the same field in QED?

I know in classical field theory we have the electromagnetic field. And Maxwell's equations show how electromagnetic radiation can propagate through empty space. I also have been reading about QED ...
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Physical meaning of the coupling matrix in Fermi golden rule

I am calculating the energy transfer rate using Fermi golden rule where the coupling matrix $M$ is obtained using second order pertubation method. $$ \Gamma_{tran}=\frac{2\pi}{\hslash}|M|^{2}\rho$$ ...
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How do photons mediate (or create) a force?

Is there a somewhat intuitive explanation as to why the exchange of a photon between two particles causes a force between those particles? Is there a difference in the way massless and massive ...
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Positronium energy level in QED

I'd like to know if it is possible to compute positronium mass and lifetime from a QED approach. I'm searching for some literature on how to treat resonances in QED (or general QFT) ; most of the ...
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Energy conservation if photon absorbed below resonance

Suppose I have some quantum system (like atom) with excitation energy $E_{exc}$ which is homogeneously broadened due to finite lifetime. I shine light with narrow spectrum centred around energy ...
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Correction of arrow of particle direction

I have seen a stamp of Richard Feynman where Feynman hold the famous Feynman diagram. But is there any problem of the direction of arrow?
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Invariance of the QED Lagrangian under charge conjugation

Is it true that the QED Lagrangian $$\mathcal{L} = \bar{\psi}(i\gamma^\mu D_\mu-m) \psi $$ is invariant under charge conjugation? $$\begin{align} \psi &\mapsto -i(\gamma^0 \gamma^2 \psi)^T\\ ...
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What are some practical things one can do with classical electrodynamics and QED?

Many basic types of physics have ready and obvious everyday applications. For instance, basic electromagnetism vector calculus can give great insights into how something as simple as a bar magnate ...
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Basic QED - How are conserved charges expressions throught ladder operators derived?

I can't find this in similar questions, and I must be missing something very basilar since I can't find this in any textbook or online note: they just skip the passage. So, from my course's notes, we ...
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Why quantum electrodynamics? [duplicate]

Most of the people seem pretty much content with classical electromagnetic theory .And most of the applications use classical EM theory .However, in such situations I would like to know what was the ...
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How the experimental charge $e=1.60217657 × 10^{-19} C$ has precisely this value?

The coupling constant that we measured in "arbitrarily" low energy is $e=1.60217657 × 10^{-19} C$. How this is presented in Renormalization Group flow in charge coupling space? Why the action of the ...
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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 ...
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Converting mode expansion to an integral in an Cavity

Assuming the cavity length is large, can we convert the summation over cavity EM modes to an integral form? In that case is it reasonable to do below conversion? p is the mode number.
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What are the electromagnetic fields of a photon?

I'm looking for expressions for the electromagnetic fields (preferably $E$ and $B$) of a typical photon which is localised in space to some extent (i.e. I'm not interested in the infinite plane wave ...
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How do I calculate a Feynman diagram with one loop?

I'm following Peskin & Schroeder and I'm trying to calculate the momentum space representation for the following diagram, Q4 in this link. Paper The loop is what's causing me problems. I'm not ...
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Can we measure the electron spin independently of its magnetic moment?

What experimental evidence do we have for the intrinsic angular momentum of the electron (its spin)? I am specifically interested in whether we have a value for this that is independent of the ...
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Conservation of energy and momentum in photoelectric effect

Sometimes it is shown that in a Compton scattering it is not possible that the photon transfers all it's momentum and energy to the electron, see for example here: If one assumes complete energy and ...
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Why is the frequency bandwidth of the environment important for Markovianity?

In the derivation of Spontaneous Emission in two level systems in Quantum Optics (be it Wigner Weisskopf or a different approach, such as density operators to find the master equation), one makes ...
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If 2 photons collided head on, what would happen? [duplicate]

If 2 photons, in perfect synch (frequency, amplitude, etc. were all equal) and they collided head on, what would happen? Would they pass right through each other? Would they interfere, then go back to ...
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Is colour a purely quantum effect?

If the colour of an object is determined by the wave-lengths of light that is absorbs and reflects (?) then can colour be described as a purely quantum effect (i.e. without quantum effects an objects ...
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Mølller scattering

I came across Mølller scattering today (which is just a fancy name for electron-electron scattering. I'm confused as to why there are two tree level Feynman diagrams for this process: Check out the ...
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The contraction of fermion field in 1+1-dimensional massless QED

My question comes from the textbook by Peskin & Schroeder, the integral (19.26): $$\begin{align} \int \frac{d^2 k}{(2\pi)^2}\! e^{- i k\cdot (y-z)}\frac{i \not{k}}{k^2} = -\not\partial ...
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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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Thomson scattering on the elections does not produce any circular polarization?

All references on CMB polarization has this statement as if it is a trivial fact. But I have to admit that I completely don't understand what this sentence is telling us.
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Charge operator for Dirac spinor

In QED, the gauge transformation which acts upon a fermionic field $\psi$ is $$\psi'(x)= e^{i \alpha(x) Q}\psi(x)$$ where $Q$ is the charge operator. Most of the time it's just written as $$\psi'(x)= ...
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Free Electromagnetic field in Lorenz gauge

To get rid of the extra term in the QED Lagrangian we need to redefine the electromagnetic four-vector: $A^{\mu} \rightarrow A^{\mu} - \frac{1}{c} \partial_{\mu} a(x)$ where $a(x)$ is the function ...
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Electro-magnetic wave propagation in vacum

I was wondering what will the EM wave propagation including virtual particle pairs existence look like. When electric field face virtual pair it should make the lowest state energy the most ...
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Counting d.o.f. and gauge fixing $A_{\mu}$ and $\psi$ in $D$-dimensions

Setup: Let us assume we are in $D$-dimensional Minkowski space-time where $D=d+1$. Consider a free Abelian gauge theory. Then the electromagnetic field will satisfy $$\partial_{\mu}F^{\mu \nu}=0 ...
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Tape as a X-Ray Source

A couple years ago I ran upon a YouTube video demonstrating how researchers used x-rays given off by tearing tape off its spindle in hopes to miniaturized and cheapen future x-ray devices. As of ...
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Why Lagrangian of electromagnetism with Lorenz Gauge evolve Klein Gordon equation?

Simply Lagrangian without a source for Maxwell equation is $$ L = -\frac{1}{4}F^{\mu\nu}F_{\mu\nu} $$ Also Lorenz Gauge condition is $$ \partial_{\mu}A^{\mu}=0 $$ and if so I can briefly add this ...
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Calculation of the Abelian Induced Chern-Simons Term

In Gerald Dunne's paper "Aspects of Chern-Simons Theory" (http://arxiv.org/abs/hep-th/9902115) I'm a little confused as to how equation (225) on page 53 is obtained. Equation (225): ...
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Why very strong fields are required for a photon to split?

Photon splitting does not occur in free space as energy and momentum cannot be conserved in any Lorentz frame. But it does occur in the presence of a strong field. Consider the example of a Magnetar. ...
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Fine structure constant definition

The fine structure constant is usually defined using $e$, $h$ ,$c$ ... However, from QED, we know it cannot be derived but only experimentally measured. Does that mean the usual definition we use in ...
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Linear and circular polarization in quantization of the EM field

I am going through the "Quantization of the EM field" in Chapter 7 of Sakurai's Modern Quantum Mechanics, which basically goes like: The vector potential satisfies wave function $\nabla^2\mathbf ...
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The fine structure constant - can it genuinely be a random variable?

The question Does it make sense, and are there physical reasons to think about the fine structure constant as a (very concentrated) probability distribution rather than a single real number? ...
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QCD and QED with unlimited computational power - how precise are they going to be?

My question is about quantum algorithms for QED (quantum electrodynamics) computations related to the fine structure constants. Such computations (as explained to me) amounts to computing Taylor-like ...
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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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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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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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Isn't the Coulomb interaction a photon interaction between two charges?

Isn't the Coulomb interaction a photon interaction between two charges? if yes then what does the following text mean? (Many-particle Physics by Gerald D. Mahan.)
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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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Aren't $\phi^4$ composite operators?

I have this trouble with terminology. I wonder why authors introduce the concept of composite operators after they've already talked about eg phi four theory, it phi cubed. Aren't these operators ...
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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 ...