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20 votes
Accepted

Is there a second-order non-linear addition to Maxwell's equations?

In Quantum Electrodynamics by A. I. Akhiezer; V. B. Berestetskii, photon-photon scattering is considered in paragraph 54, and the effective classical Lagrangian for nonlinear vacuum electrodynamics ...
E. Anikin's user avatar
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14 votes

Is there a second-order non-linear addition to Maxwell's equations?

In addition to what the other answer already mentions, the non-linear extension required to include QED effects classically can also be found in [Jackson]. But the claim the question makes, that &...
Jos Bergervoet's user avatar
9 votes

Photon propagator

Right off the bat, to answer your first question $\Pi^{\mu\nu}(p)$ is the Fourier transform of $\langle 0| T\{A_{\mu}(x) A_{\nu}(x') \} |0 \rangle$. Usually $\Pi^{\mu\nu}(p)$ would be referred to as ...
Josh Newey's user avatar
7 votes

Is there a second-order non-linear addition to Maxwell's equations?

Good answers. I just want to add that as I commented electromagnetism is strictly linear without coupling to charged if there ís coupling to charges or spins then upon integrating out the virtual ...
my2cts's user avatar
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3 votes
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$ \pi^0\to \gamma\gamma$ parity conservation

As @Cosmas Zachos said in his comment, the Levi-Civita pseudotensor $\epsilon$ has negative parity. But why? This is the case because $\epsilon_{\mu\nu\rho\sigma} := \sqrt{-g}\ \varepsilon_{\mu\nu\rho\...
Gabriel Ybarra Marcaida's user avatar
2 votes

In dispersive readout of a qubit coupled to a resonator, how is the measured phase shift used to determine the resonant frequency of the resonator?

In dispersive readout, there are two ways to readout the state of your qubit: amplitude and phase readout, see Chapter V in this great guide on superconducting qubits. In the first case, the probe ...
DisposableGuy's user avatar
2 votes

How is light interference explained with photons?

Now, if we model light as collections of photons, how is light interference explained? It is explained the same as classically. Classically there is an electromagnetic field that obeys Maxwell’s ...
Dale's user avatar
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1 vote
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Some calculation in Schwartz's Quantum field theory eq. (16.39)

What is definition of $\Pi_2^{\mu \nu}$? What do we call such an object? It is defined in (16.24), the vacuum polarization tensor, after which the chapter is named. What is $\gamma_E$? As your ...
Cosmas Zachos's user avatar
1 vote

Does the creation operators for photons with different polarization commute?

Boson creation operators always commute, i.e. $[a_\alpha^\dagger, a_\beta^\dagger]=0$ for all $\alpha,\beta$. In fact, $[a_\alpha^\dagger,a_\beta]=0$ if $\alpha\ne \beta$ as well provided that $\...
ZeroTheHero's user avatar
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