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Starting from the boundary condition $$\partial^{\sigma}X^{\mu}(\tau,0)=0$$ and lowering the index on the derivative using the metric gives $$\gamma^{\sigma\tau}\partial_{\tau}X^{\mu}(\tau,0)+\gamma^{\sigma\sigma}\partial_{\sigma}X^{\mu}(\tau,0) =0.$$ Apparently Polchinski wants to express this in terms of the metric $\gamma_{ab}$ with its indices ...

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In a viscous fluid the shear stress is proportional to the velocity gradient. $\sigma=\eta \frac{dv}{dy}$ where $\eta$ is the viscosity, and $v$ is the fluid speed at right angles to the $y$ axis. Therefore as the small distance $dy$ tends to zero, the change of fluid speed $dv$ also tends to zero, for any non-zero viscosity. Let us now follow Navier ...

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Usually we think of friction as something like this (not a formal definition, but I think it's close enough to be understood as "friction"): when two objects move past one another and are in contact, the differential velocity between them leads to a force we call "friction" At the boundary between a liquid and a solid, if we permit a different velocity ...

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The little group is the subgroup of the Lorentz group that leaves an arbitrary four-momentum vector invariant, i.e. for an element of the group $g$ and momentum $V$ we have $gV=V$. This group is in general different for massive and massless particles. If you now find that the little group of your holomorphic primaries corresponds to that of massive states, ...

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You should not imagine a virtual photon as an individual object wandering from one charged particle to another. This picture is simply inapplicable. Unfortunately, Feynman diagrams mislead people to imagine such things. Actually, Feynman diagrams are good for calculation and bad for imagination. Feynman diagrams have been introduced to help physicists to ...

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All charged particles emit photons which are uncharged. They may, given the right boundary conditions. So how does the photon "know" that it's leaving one kind of charge and "lands" on another? What you are describing here is a "virtual photon", an interaction between two charged particles. There is the complicated way, i.e. mathematical ...

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You can think of a photon as a quanta of energy. In that case, it can impart its kinetic energy to a charged particle, or, vice vers, a unit of energy can be released when a charged particles slows down and loses kinetic energy

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The charge is distributed uniformly on a spherical surface, but that is a function of the high degree of symmetry on the situation. In general the charge tends to accumulate most strongly near pointy bits and most weakly in depressions in the surface. There are several way to understand this. My favorite is not necessarily the most helpful for a beginner, ...

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I believe that for an ordinary conductor, there is nothing special for a static magnetic field. But this relates only to the electrical properties of that conductor - many material have some magnetic properties as week, and those would of course modify the B field. But for the purpose of this question the B field follows the dipole field "in free space" - no ...

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