# 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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^...
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 ...