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I find the "intuitive number" argument to be very misleading. One argument against it is... what is $N$? In fact the state of the electrostatic field around a point particle is a coherent state, which is a superposition of states with different numbers of particles. So it's not really possible to say that there are a definite number of photons &...
3
This is the lowest Feynman diagram showing the exchange of virtual photons in electron electron scattering
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Depending on the problem one would be studying with proton-proton elastic scattering, a similar diagram with "p" instead of "e" would be used for the electromagnetic interaction.
Considering that the protons are composed of charged ...
3
In a nutshell, to recover the static Yukawa potential between 2 points in 3 spatial dimensions, one should consider the 2-point correlation function/Greens function$^1$
$$G(\vec{r})
~=~\frac{e^{-mr}}{4\pi r}, \qquad (-\vec{\nabla}^2+m^2)G(\vec{r})~=~\delta^3(\vec{r}),\tag{1}
$$
in the static picture, cf. e.g. Wikipedia & this Phys.SE post.
Example: For ...
3
Equivalence of Maxwell and electric field operator in the Coulomb gauge (minimal and polar coupling)
To show the two formulations are equivalent, note that in Coulomb gauge, $A^0=0$ so $E_i = \partial_i A_0 - \partial_t A_i = - \dot{A}_i$.
Then using $p_i = m \dot{x}_i$, and defining $H_A$ to be the Hamilonian written in terms of $A$ and $H_E$ the Hamilontian written in terms of $E$, we have
\begin{eqnarray}
H_A &=& -\frac{e}{m}p^i A_i \\
&=&...
3
Energy conservation holds. The two photons you start with, they together need to have at least as much energy as the restmass of the electron and positron. So for usual meanings of the word "weak": no, radio waves in a weak electric field do not convert.
2
The short answer: the relevant lifetime is not the one of an individual excitation, but the first-order coherence time, the timescale at which the phase diffuses.
The longer answer is very interesting. On the quantum level, both the photons coming in and out of the cavity are described by a Lindblad process. For the gain, the jump operators are $\sqrt{R}a^\...
1
At a temperature of 1 keV, the electromagnetic field (best described in that circumstance as a gas of photons) is able to approach thermal equilibrium with the electron-positron field. See this superficially-unrelated related question for a practical consequence.
In a universe where the cosmological constant were a million times larger than ours, my ...
1
Emission means different things when talking about the lifetime of an excited state and about stimulated emission.
Finite lifetime of an excited state means that, if an atom in an excited state is left alone, it will eventually relax to the ground state, spontaneously emitting a photon. This results from the fact that we have an infinite number of states ...
1
an electron mostly acts like a wave. An atomic electron spreads out into cloud-like wave shapes called "orbitals". If you look closely at the various orbitals of an atom (for instance, the hydrogen atom), you see that they all overlap in space. Therefore, when an electron transitions from one atomic energy level to another energy level, it does not ...
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