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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Deriving non-relativistic potentials from QFT

Some systems, like atoms, are described well by quantum mechanics, where one just gives the Hamiltonian in the form $H=T+V$ and computes the eigenvalues and eigenvectors of this operator to figure out ...
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Running of the fine structure constant: meaning of $\alpha(Q^2=0)$?

In Measurement of the Running of the Fine-Structure Constant, the L3 collaborations writes At zero momentum transfer, the QED fine structure constant $\alpha(0)$ is very accurately known from the ...
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Numerical solution to integro-differential equation (Wigner Weisskopf Problem)

The time dynamics of an atom interacting with a reservoir of spectral density $J(\omega)$ are obtained by solving the following integro-differential equation $[1]$: $$ \dot{c}(t) = \int_0^t dt'\int_0^{...
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Does the neutrino interact with the photon?

I know that the straight answer is no, but in my EFT course, where we're interested in nonrenormalizable operators of the Lagrangian, things aren't so straightforward. The non-minimal QED Lagrangian ...
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Explicit check of Ward identity (Peskin & Schroeder p. 160)

I am trying to check explicitly that the (Compton) amplitude $$i\mathcal{M} = -ie^2\epsilon^*_\mu(k’)\epsilon_\nu(k)\bar u(p’)\left[\frac{\gamma^\mu \not k\gamma^\nu + 2\gamma^\mu p^\nu}{2p\cdot k}+\...
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Free energy from the vacuum?

An electric field with an intensity of the Schwinger limit $$E=\frac{m_e^2c^3}{e\hbar} \approx 10^{18} \hbox{ V/m}$$ is strong enough to create electron-positron pairs out of the vacuum by separating ...
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Complex Coupling Strength in Light-Matter Interaction Hamiltonian

The quantised electric field operator is given by : $$ \hat{\mathbf{E}}(\mathbf{r},t) = i\sum_{\xi}E_{\xi}\left(\mathbf{u}_{\xi}(\mathbf{r})a_{\xi}-\mathbf{u}^*(\mathbf{r})a_{\xi}^{†}\right) $$ where ...
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Choosing the polarization vectors, Quantization of EM field

In Sakurai, Modern Quantum Mechanics 3rd edition, page 465, the book writes: The set of solutions to $$\nabla^2\boldsymbol{A}-\frac{1}{c^2}\frac{\partial^2\boldsymbol{A}}{\partial t^2}=0\;\;\;\;\;\;\;\...
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Can we say that the following equation has substantially the same physical meaning as the Dirac equation?

Dirac's equation is given by $$\left[\beta mc^2-i\hbar\frac{\partial}{\partial t}+c \sum ^3_{n=1} \alpha_n p_n\right]\psi(\vec{x},t)=0\tag1$$ Here, $\alpha_n$ in Eq. (1) is an operator having a ...
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In and out states of scattering in Asymptotically flat spacetimes

I am reading a paper called "New symmetries of massless QED", written by Temple He, Prahar Mitra, Achilleas P. Porfyriadis and Andrew Strominger (https://arxiv.org/abs/1407.3789). At some ...
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Solving Periodic Time Dependent Hamiltonians

For a general time dependent Hamiltonian, if the Hamiltonian at two different times $t_1,\,t_2$ satisfies $$\left[ \hat{H}(t_1),\hat{H}(t_2) \right]=0,$$ then the time evolution operator is $\hat{U}(t)...
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Purcell effect for large cavities

The model of interest is a 2-level system (e.g. an atomic transition) inside a damped single-mode cavity. The purcell effect states that the atomic decay rate inside the cavity $\Gamma_{cav}$, on ...
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Advantages of using the potentials $A$ and $\phi$ instead of the fields $E$ and $B$ [duplicate]

I'm taking a quantum mechanics course and we briefly reviewed some facts of ED, namely the Maxwell equations and their equivalent version by expressing the electric field $E$ and magnetic field $B$ ...
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Wick theorem and explicit vanishing of $\text{vacuum}\to e\bar{e}$

I want to see explicitly how the transition amplitude for $\text{vacuum}\to e\bar{e}$ vanishes in QED but I'm struggling with Wick's theorem . I take $|i\rangle=|0\rangle$ and $|f\rangle=b^\dagger(\...
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Are there still objections against the renormalizability of QED?

I read that even Dirac in 1975 and Feynman in 1986 had concerns with the renormalizability of QED: Renormalization. Which objections did they make? What is the present state concerning their ...
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Conventions Consistency For the Dirac Field

I am writting a text and I try to be consistent with my definitions. I have expanded my fields in modes in the following way $$\psi(x)=\int\frac{d^3\vec{p}}{(2\pi)^3\sqrt{2p^0}}\sum_s\bigg(u_s(\vec{p})...
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A question about virtual particle

I am currently learning QFT and there is always a question to haunt me. As I know, virtual particles represent those propagators in the Feynman diagram which could be off-shell. My understanding is ...
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5 votes
2 answers
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Difference between two forms of the electric field operator

I'm currently taking a course in Quantum-optics, focusing primarily on the book Introductory to quantum optics by C. Gerry & P. Knight. In the book they first present the quantization of a single ...
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Why do we need to make sense of QED in continuous spacetime anyway?

QED is an approximate description of reality. Even if it did give finite predictions in the continuum limit, those predictions would've been incorrect anyway! Newtonian gravity does give finite ...
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Does photon-photon scattering influence classical vacuum E&M dynamics?

At a purely classical level, Maxwell's equations are completely linear, and associated with a linear coupling to a conserved current in the electrodynamical Lagrangian. When this Lagrangian is ...
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Why is the Anomalous magnetic dipole moment defined as half the extra contribution to the $g$-factor?

Was there a reason Julian Schwinger or Richard Feynman officially defined the anomalous magnetic moment as half of the extra $g$-factor? $$ a = \frac{g-2}{2} $$ (equation is from the Wikipedia article ...
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3 votes
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How the concept of "wave function of atom" in Bose-Einstein condensate should be interpreted from perspective of quantum field theory?

A typical description of Bose-Einstein condensate goes along the line of "multiple atoms in the same ground state can be described by the same wave function". But hold on. Atoms are not ...
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Exact propagator - 1pI diagrams

Above diagram can be written in terms of series: $$i\Delta = -\frac{i}{p^2 + m^2} + \Big(-\frac{i}{p^2 + m^2}\Big)(i\Pi)\Big(-\frac{i}{p^2 + m^2}\Big)+ \Big(-\frac{i}{p^2 + m^2}\Big)(i\Pi)\Big(-\frac{...
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1 vote
2 answers
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Electron Muon scattering in the CM frame, question about the energy

I calculated the spin-averaged amplitude for the $e^{-}\mu^{-} \rightarrow e^{-}\mu^{-}$ scattering in the CM frame in the high energy regime($m_{e}$,$m_{\mu} \rightarrow 0$) following the hints ...
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1 vote
0 answers
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Does a free proton shrink when accelerated?

Reading about the charge radius of the proton and proton radius puzzle I started wondering if the cross section and therefore also the charge radius (i.e. size of proton) changes or more specifically ...
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1 vote
1 answer
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Faddeev-Kulish Asymptotic Dynamics Question

I am reading a paper by Faddeev and Kulish ("Asymptotic conditions and infrared divergences in QED" written in 1970) and I have a question regarding the nonrelativistic problem of Coulomb ...
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Why the electron having a relative light mass $511keV$ is so small, upper limit $10^{-18}$m, in the SM? [duplicate]

Usually in particle physics larger mass refers to a smaller cross-section of a particle or atom thus a smaller sized particle. How a so relative light mass particle only $511\,\mathrm{keV}$ can be so ...
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2 answers
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Why does the proton have the same elementary charge value $e$ as the electron? [duplicate]

Maybe a silly question but I am looking for an analytic explanation of it. I think I already have one but I want to see if there is a better one, more fundamental? What does it mean fundamentally ...
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1 vote
1 answer
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Can Compton scattering occur between a photon and a neutrally charged particle?

Compton scattering occurs because of the particle-like nature of light, but does it occur between photons and charged particles only? Is it impossible for Compton scattering to occur between a photon ...
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0 answers
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Change in photon production rates due to finite temperature / a QED plasma?

I have the following question: In a QED plasma, the photon technically gains a "mass" due to a change in its dispersion relations. I was wondering, if the photon also acts as massive during ...
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Running of the fine structure constant

In Measurement of the Running of the Fine-Structure Constant, the L3 collaboration reports their fine structure constant data for various values of momentum transfer which they call $Q^2$. This is ...
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How are Hydrogen Atoms Described in Standard Model? [closed]

Specifically, in order to calculate the quantities like emissivity or the cross section of photon resonant scattering by hydrogen atoms, what logical deduction route should we follow, starting from ...
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Vector potential of photon in quantum field theory

In quantum field theory the solution to Maxwell's equation is given by: $$ A^\mu(x)=\underbrace{\sum_{r,\mathbf k}\frac{1}{\sqrt{2V\omega_{\mathbf k}}}\varepsilon_r^\mu(\mathbf k)a_r(\mathbf k)e^{-ikx}...
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How does QED explain the circular magnetic field around a straight conductor?

Since Maxwell's equations are phenomenological, I'm looking for the actual deep reason why the magnetic field is oriented circularly around a straight conductor. Could anybody knowledgeable on quantum ...
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Linear independence of Electromagnetic Field polarization

In electromagnetism, we are free to choose a gauge such that $\partial_{\mu}A(x_\mu) = 0$. This, along with the mass on-shell condition for a massless gauge field, implies that there are only 2 ...
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2 answers
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What scale are Maxwell's Equations valid?

Both Maxwell's equations and quantum mechanics are used to describe the behavior of electrons in circuits. I am confused on the interlinking between the two and the dividing line between when you use ...
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2 votes
0 answers
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Electroweak theory Landau pole

It is known that non-asymptotically free theories like Quantum Electrodynamics or Scalar field with quartic interactions ($\phi^4$) have a landau pole which mainly investigated through lattice ...
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What is the theoretical limit on accuracy of an idealized photon detector?

I know that Heisenberg's Uncertainty Principle and the Observer Effect mean there is a fundamental limit to the accuracy with which the values for certain pairs of physical quantities of particles (...
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Why do diamagnetic rods align perpendicular to the field?

My textbook says that Diamagnetic substances align their longest axis perpendicular to the field in uniform magnetic field while paramagnetic substances align their longest axis parallel to the field. ...
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1 vote
1 answer
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Modified photon propagator with a fluctuating current

I am studying a paper on the effects in bound-state QED coming from nuclear dynamics, and I am struggling to understand one basic derivation. The authors introduce a modified photon propagator $$ \tag{...
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17 votes
6 answers
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What does it mean that dimensionless physical constants cannot be calculated but only measured?

I have read a passage in Wikipedia about the List of unsolved problems in physics and dimensionless physical constants: Dimensionless physical constants: At the present time, the values of various ...
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2 votes
1 answer
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What is the Noether continuous symmetry associated with the conservation of total particle number for a free complex Klein-Gordon field?

Obviously I know that the $U(1)$ symmetry is associated with the (number of particles - number of antiparticles) conservation. However I thought, by Nother's theorem, that every conserved quantity ...
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What is the interpretation of the quantum field operator solving the Klein-Gordon equation?

Does the quantum field operator $\hat \psi^\dagger(x)$ solving the KGE mean that we should think that every quantum field configuration evolves under a KGE field equation. Or do we just understand it ...
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Lamb shift at the level of four-potential seems to violate causality

In QED, it is well known that in a suitable renormalization scheme, and in a static case, the potential energy taking into account the Lamb shift of the electron around the nucleus of charge $Ze$ in a ...
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1 vote
5 answers
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Force between two protons

Yesterday my teacher was teaching about the production of photons, he told that photons are produced when the electron move from a higher energy level to a lower energy level then suddenly a idea ...
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2 votes
0 answers
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Are canonical commutation relations only valid for non-relativistic QM? [closed]

Other questions (such as What is the "secret " behind canonical quantization?) seem to suggest that ultimatley, the motivation behind imposing the canonical commutaiton relation $$[x,p]=i\...
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1 vote
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Electron positron annihilation to more the 3 photons

I understood why a single photon can't be released from the annihilation of an electron and positron and that the common cases are 2 and 3 photons. I have two thing's I'm unsure of: why is the ...
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2 votes
0 answers
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Why Lorentzian momentum corresponds to $1/$length?

I'm reading Peskin & Schroeder's QFT, the effective coupling related with QED, is given by (7.96): \begin{align} \alpha_{\rm eff}(q^2)=\frac{\alpha}{1-\frac{\alpha}{3\pi}\log \left( \frac{-q^2}{Am^...
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Virtual photons

Is it true what is said about photons that carry electromagnetic force or field? are they virtual photons too? Where exist real photons? I don't understand the concept of virtual photon, in ...
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3 votes
3 answers
551 views

A problem with QED

I have a small problem with the understanding of QED. The equations of motion in QED are $\square A^\mu=e\bar{\psi}\gamma^\mu\psi$ $\left(i\gamma^\mu\partial_\mu-m\right)\psi=e\gamma^\mu A_\mu\psi$ If ...
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