this latex template also uses this package which seems to affect the font: \usepackage{mathptmx} % d. ...in a simple roman face except where indicated below (§3).
@SillyGoose you can always go back to old Newtonian mechanics with every single particle in physical space instead of the combined configuration space~
@SillyGoose KathyLovesPhysics covers the original papers of E&M. Extremely amazing stuff.
@SillyGoose M I A O ~ ~
@SillyGoose It cannot be, because the completion of putting together Maxwell's equations were all done without the conception of SR nor QM. Of course, if you want a modern account that emphasises how SR and QM are actually really needed for Maxwell's equations to be as they are, you might find one, but it is not how we got here.
Also, ACM's reply to you there is undoubtedly correct, but he omitted an important aspect, probably because everybody talks about this: The spin-statistics theorem says that the spin one of photons makes it so that photons obey Bose-Einstein statistics, and this amplifies the collective wave aspects, so that the classical wave aspects are salient. Contrasted with electrons obeying Fermi-Dirac statistics, which amplifies individual particle aspects.
@SillyGoose burn this. Either define the 1-form with a minus sign, or define the 2-form with the opposite sign. Nobody should be taking the negative of a exterior derivative as a convention.
@SillyGoose horrifying mistake, but it is also the kind of mistake that would be completely prevented if you had concrete applications of all the various entities involved, instead of an abstract-only learning. It is not just the metric that is a symmetric tensor. There are plenty of others in physics.
@JohnRennie i think if you write it out as you did and then use the metric to lower the index of the second term and then differentiate using product rule you will get your wanted result
I think $$\frac{\partial}{(\partial_{\mu}\phi)}\frac{1}{2}(\partial_\mu\phi)^2 = \frac{2}{2}\frac{\partial}{(\partial_{\mu}\phi)}(\partial_\mu\phi)(\partial^{u}\phi)$$
In particular, it is that $\frac12(\partial_\mu\phi)^2=\frac12\partial_\alpha\phi g^{\alpha\beta}\partial_\beta\phi$ so that the derivative denominator that is $\partial\partial_\mu\phi$ with the two partials, converts first just one, and then the other, into a kronecker delta. Then the two parts are the same thing, and cancel away with the half.
@Obliv why do you have a dangling $\partial^\mu$ at the end?
@SillyGoose This package defines Adobe Times Roman (or equivalent) as default text font, and provides maths support using glyphs from the Symbol, Chancery and Computer Modern fonts together with letters, etc., from Times Roman. It supersedes both the original times and the mathptm packages.
@JohnRennie I have no idea what's going on physically/mathematically but it seems to me if you plug in that identity and then take the derivative, the term $\partial_{\mu}\phi$ vanishes and we have $(\partial^u\phi)$ kinda like $\frac{\partial}{\partial x}xy = y$ where $x = \partial_{\mu}\phi$ and $y = \partial^u\phi$
if you wanted to do the calculation systematically, you should lower all indices via the metric tensor and then apply usual calculus to take derivatives
@Obliv technically, none of it is of any importance. Plenty of physicists get by with none of these. But it is very helpful to know some of these maths
@Relativisticcucumber incomprehensible utterances are a hallmark of eldritch beings a la Lovecraft - once you understand them, you typically go insane, i. e. become a physicist
We have geese just chillin on campus snacking on the grass and they're so docile/used to students just walking near them.. but I have to remind myself that they're actually just cobra chickens..
my supervisor believes that nobody really understands physics and that people just say random things that they think are related to what is being discussed
i think thats a him problem
i have begun to dig too deep into his endeavors. i have found that 30% of his citations are from himself. on average, 70% of the citations of his papers are by him
or "on median" im not sure which i should say. selecting papers at random, examining who they have been cited by, 70% of it is him is what i mean
@Relativisticcucumber omg that is something that I would consider for reporting to the university. Can you, like, pivot to another supervisor or something? Very very scary
That is also why niche parts of science deserve scrutiny. It is much more difficult to make shit up in hotly contested experimental areas, whereas if you write shit in a niche area that nobody really cares about, you can hide quite well
yeah well this guy is quantum info but hes not that big. it just bothers me bc he refers to himself as someone who is big in the field and its just annoying bc i wanna be like bro i know u r just a citation machine with urself who r u fooling
but it does make me sad that science is corrupt. but its just smth to learn to navigate i guess : ////
When miao miao jumped out of QC to join this company, the physics people who heard what miao miao was doing in QC, all agreed that miao miao dodged a bullet. And then the people who touched QC before, added their own QC horror stories
@Relativisticcucumber anyway, your latest question about BEC, im not sure what you want more than the fact that Bose-Einstein statistics favour a LOT of particles sharing the same state.
