Recent content by Pnin

I want to follow the Lienard-Wiechert potential derivation in Robert Wald's E-M book, page 179. I do not understand $$dX(t_\text{ret})/dt$$ on the right side. I assume the chain rule is applied, but I can't see how. $$ \frac{\partial[x'^i - X^i(t - |\mathbf x - \mathbf x'|/c)]}{\partial x'^j} =...

This is from Coleman Lectures on Relativity, p.63. I understand that he uses integration by parts, but just can't see how he gets to the second equation. (In problem 3.1 he suggest to take a particular entry in 3.1 to make that more obvious, but that does not help me.)

thanks!

I want to approximate the logarithm of the Binomial coefficient log (n!/ ((n - m)! m!) with the the Stirling approximation log x! ≈ x log x - x I got n log n - m log m - (n - m) log(n - m) but I want (n - m) log (n/(n - m)) + m log (n/m) Can someone help how to transform the first...

Ok. Then let's use this standard meter stick in Paris, instead. Could I still not measure a different speed of light in principle, because the speed of light is a dimensional universal constant? Which means that a different speed of light would also imply different radii of the atoms that make...

I do not follow. When we measure the speed of light in meters and seconds we get 299792458 m/s. We measure it. My question (rephrased): what would the world look like when would measure ligth traveling at 2 m/s instead?

If Planck constant h and light speed constant c were (very) different, would we notice it? (I know we can change units and make h and c take any numerical value we like. But let‘s stick with one set of units.) I assume rulers, clocks, coupling constants, all dimensionless constants would...

Great! Thanks, Peter.

From Tong gravity notes pdf page 32 : We see from the picture that there are more ways to “go to infinity” in a null direction than in a timelike or spacelike direction. This is one of the characteristic features of Minkowski space. I read that also elsewhere. Why are there many null-like...

Unfortunately, still a bit unclear. If f'(t) = z/(1-zt)^2, shouldn't it be f(t) = z⋅(z/(1-zt)? Also, what next? I need to integrate one more time by parts. But I have a new 1/t term. I want that term in my final result (4), not now. Integrating by parts without the 1/t would give me...

Thanks, mfb. Much appreciated.

I assume repeated (twice) integration by parts. That makes me believe the integral in (3) can be morphed into the integral in (1). With surface terms disappearing somehow. But where does the sum sigma come from?

Good idea. How do I do that? Or could some admin move my question? thank you

This is from Horatio Nastase "Intro to Quantum Field Theory" book (Cambridge University Press, 2019) , chapter 59. The reader is supposed to massage equation (3) into equation (4) with the help of the given polylogarithm formulas (1) and (2). I do not see at all how that's possible...

Ok. I never saw that trick before. But if I had written another number I would not have gotten the desired result, the harmonic series. So is that really a legal trick which allows you getting different values from a definite integral?