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5

A comment about coherence in general I find the definition of coherence as some sort of "unrelated phase" problematic for a couple of reasons: This formulation somewhat implies that coherence is discrete, i.e. there is incoherent and coherent. Of course that is not true, you can have a continuum partially coherent states. But what quantity are you going ...


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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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We can obtain Coulomb's law in the non-relativistic limit of the tree-level QED interaction, cf. this question. The Biot-Savart law is a consequence of Maxwell's equations, cf. this question. And Coulomb's law together with special relativity is sufficient to derive Maxwell's equation, cf. this question. So, altogether, yes, we might say that we can derive ...


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That's a naïve point of view; however there is a rigorous construction of "wavefunctionals". It is a point of view initiated by Segal and then continued by Nelson and called the (free) Markoff field. It is rigorously understood for free fields, and in some special case also for interacting ones. The idea is related to the fact that it is possible to link ...


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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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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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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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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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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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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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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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I will address: My question - Does not photon, which is supposed to be quantum of electro-magnetic field, interact with an electron "electromagnetically"? A photon and an electron are elementary particles, quantum mecanical entities. Probabilities of interaction in quantum mechanics are calculated from the wave functions of the system in QED, using ...



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