Recent content by Adgorn

I'm trying to explicitly find a projective unitary scalar representation of the Galilean group. I'll denote a generic element of the group by ##(a, {\bf b},R, {\bf v})##, corresponding respectively to time translation, space translation, rotation and boosts. In a representation with central...

Never mind, I immediately realized upon hitting "post" that complex conjugation switches the order of Grassmann numbers. Better late then never.

I've managed to account for all the terms except for two, which seem to have a minus sign I cannot get rid of. When expanding the variation, one of them comes from the ##\phi## variation: $$-i \partial^\mu \phi \epsilon^\dagger \sigma^2 \partial_\mu \chi^* =-i \partial^\mu \phi \partial_\mu...

The class is using Gaussian units, sorry for not being clear on that. It looks like the examiner was wrong, I just wanted to be sure. The official answer was indeed ##\gamma T## where ##T## is the non-relativistic answer, which I could not match with my answer because I mistook ##v = \frac R...

My solution was as follows: $$\frac {d\overrightarrow p} {dt}=q \frac {\overrightarrow v} {c}\times \overrightarrow B_0$$ The movement is in the ##[yz]## plane so ##|\overrightarrow v\times \overrightarrow B_0|=vB_0##, therefore: $$\biggr |\frac {dp} {dt}\biggr |= \frac {qvB_0} {c}.$$ On the...

That cleared it up. Thank you for the clear and illustrated answer!

In his solution, Morin solves the problem as the hint suggests: cutting the chain into small pieces, taking the component of the external forces along the curve (which is just the component of gravity here) and summing up an in integral, obtaining 0. He then claims that because the "total...

Alright, so after boiling it down to Apostol Vol 2 vs Hubbard & Hubbard I've decided to go with the latter. Having gone through previews for both books and their table of contents it seems Hubbard will surely cover everything I'll come across in my course as well as some nice bonus material...

I disagree with the notion that rigor somehow negates the utility of a solution manual. Any student is fundamentally limited in their ability to review their own solutions. First, even if one believes that one solved a problem in the most rigorous way possible, mistakes and misconceptions are...

Courses in my Uni rarely have a single book that they follow, at most they feature a list of recommended books with a stern warning that the materials of the books may not overlap the course material, and the books features are usually not as comprehensive as I want them to be. The syllabus is...

Hello everyone. I'm about to take Calc 3 next semester and am looking for a rigorous book to work with on multivariable calculus. I've gone through Spivak's "Calculus" from cover to cover and am hoping to find something with the same degree of rigor, if possible, and preferably with a solution...

Since $$\lim_{x \rightarrow 0} \frac {R_{n,0,f}(x)} {x^n}=0,$$ ##P_{n,0,g}(x)## contains only terms of degree ##\geq 1## and ##R_{n,0,g}## approaches ##0## as quickly as ##x^n##, I can most likely prove this using ##\epsilon - \delta## arguments, but that seems overly complicated. I also can't...

I mean... it is, I'm just trying to prove it. The assertion that ##du = \frac {du} {dx} \cdot dx## is what drove me to try to find the proof. I can't use this equation in a formal proof because this is just notation, it doesn't mean anything on its own since standard calculus doesn't actually...

This was actually one of the first things I tried. I took the time to prove all of these Theorems on paper and understand each stage of the proofs (and once you prove them rigorously with ##\epsilon-\delta## arguments, the intuition practically forces itself upon you). At this point I actually...

Hello everyone. First off, I'm sorry if this post is excessively long, but after tackling this for so many hours I've decided I could use some help, and I need to show everything I did to express exactly what I wish to do. Also, to be clear, this post deals with integration by substitution. Now...