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Energy loss by photons occurs in a dielectric medium when the photons interact with the atoms of which the dielectric is made. This interaction does not normally result in a red-shift of the photons, but rather an attenuation of a beam of photons due to photons being absorbed. Depending on the nature of the material and the energy of the photons, the ...


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It looks like the reaction $\gamma \to 2\gamma$ is not only dynamically forbidden (Furry's theorem), but also kinematically forbidden. As Dexter Kim points out, the only way to conserve energy and momentum is that the two photons are emitted at $0°$, in which case the angular momentum along the direction of motion is given by the coupling of the two photon ...


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It is certainly thermodynamically possible for a high energy photon to vanish and a multiplicity of lower energy photons to be created. This is observable as a cascade of events (photoelectric absorption of a photon, followed by multiple fluorescence photons) in thermalization of a high energy photon interacting with matter. It isn't a simple photon-in, ...


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It's actually quite simple. If the electromagnetic field (i.e. photons) were charged, that would imply non-linear self-interactions such as those occurring for the gluon octet that mediates the strong force. The gluonic Lagrangian takes the form $$\mathcal{L}_\text{SU(3)} = -\frac{1}{2} \, \mathrm{tr}(F^2) = -\frac{1}{4} \, \sum_{a = 1}^8 F_{\mu\nu}^a \, F_a^...


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The Lagrangians are not identical, but they only differ by a total derivative. In other words, you get from the one to the other using partial integration. For example, for the first term: $$ -\frac 1 2 (\partial_\mu A_\nu) (\partial^\mu A^\nu) = -\frac 1 2 \partial_\mu \left( A_\nu \partial^\mu A^\nu \right) + \frac 1 2 A_\nu\, \partial_\mu \partial^\mu A^\...


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Yes it is correct. The derivation in P&S is straightforward but I will expand on it a bit. The key observation is that \begin{equation} \int\frac{d^4k}{(2\pi)^4}e^{-ik\cdot(y-z)}\frac{i\gamma^{\mu}k_{\mu}}{k^2+i\epsilon} =-\gamma^{\mu}\partial_{\mu}\int\frac{d^4k}{(2\pi)^4}\frac{1}{k^2+i\epsilon}e^{-ik\cdot(y-z)}, \end{equation} where the integral on the ...


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If a particle changes flavor, it's a charged-current weak decay. Example: $n\to pe\bar\nu$. If there's a neutrino in the final state, it's a weak interaction. Decay example: $\pi^+\to\mu^+\nu$. See also neutrino scattering. If parity isn't conserved, it's a weak interaction. Examples: $K^0 \to 2\pi$ and $K^0 \to 3\pi$. Note that kaon decays and $K\...


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See, the thing is that spin is actually a vector — it has also a direction. When considering such vector in quantum mechanics, 2 observables describe it completely: its norm ($S$) and projection on one of the axis (usually, $S_z$). For a spin-$\frac12$ particle the norm is $S=\frac12$ and $S_z = \pm \frac12$. Then, for a system of 3 spin-$\frac12$ particles,...


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Couplings that change (run) with scale occur in most quantum field theories! If you want a simple example, take a scalar theory with a quadratic and a quartic interaction (https://en.wikipedia.org/wiki/Quartic_interaction). In this theory, as you go to lower energies, the mass grows and the quartic coupling goes to zero. This theory is important both in ...


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The correct keyword for this is "renormalization". And, as you said yourself, high energy physics shares this field with condensed matter. In condensed matter, you always encounter renormalization group of some kind if you are interested in critical phase transitions (which are scale invariant). Good references for this are Wikipedia and this book. ...


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If you want to consider this in terms of QED, then it is easy. Virtual pair production-annihilation is described by a vacuum bubble diagram where two propagators a contracted into a loop and there are no external legs. These kinds of diagrams are usually thrown away when we consider the partition function of the theory. And there is a good reason for that, ...


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The electron and positron are two point charges with opposite sign, and classically , as the field lines are an iconal representation of the charge, when the charge becomes zero there will be no electric field lines from the spot where the two point particles overlap. BUT electrons and positrons are quantum mechanical particles and when close enough ...


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I was puzzled by this same thing when I took QFT classes several years back. After thinking about it, the reason is so trivial as to not merit an explanation in the literature, especially Peskin and Schroeder. Look at th LHS of your first equation: $\begin{align}\sum_{s,s'}\bar{v}^{s'}_a(p_2)\gamma^\mu_{ab}u^s_b(p_1)\bar{u}^{s}_c(p_1)\gamma^\nu_{cd}v^s_d(...


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An $A_{ab}B_{bc}$ yields a $C_{ac}$. Contracting all indices, but the outer ones of your expression yields a $[(\not{p}_2-m)\gamma^\mu(\not{p}_1+m)\gamma^\nu]_{dd}$. Now executing the $dd$ contraction is just the trace.


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In modelling elementary particle interactions, Feynman diagrams are used to represent the scattering amplitude which will give the crossection for the interaction. This is a diagram for calculating the first order contribution to the elastic scattering ( taking the x axis as time, ) of an incoming e+ e- pair to an outgoing e+ e- pair. The exchanged ...


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The idea that distances have to be integer multiples of the Planck length is a common misunderstanding. The actual role of the Planck length is a bit subtler than that. In quantum mechanics, the possible observable values of a physical quantity (such as a particle's position) are the eigenvalues of a Hermitian operator associated with that quantity. But the ...


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You measure the time it takes to go from one place to another. Just like you would with a car, only you use particle detectors. (For charged particles of known mass and speed less than about 99% of the speed of light you can also measure the relationship between their energy and momentum, but that doesn't apply to neutrinos.) The speed of light is about $30\...



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