Good alternatives to Georgi's Lie Algebras in Particle Physics? I just started reading Lie Algebras in Particle Physics by Howard Georgi and I'm finding it frustratingly fuzzy. What I mean is that he often makes non-trivial statements without proof, is imprecise with definitions, and so on. However, what other books I can find seem to swing a bit too far the other way, and I simply don't have time for the most comprehensive and rigorous treatments. The ideal book would be somewhere in the middle. It should be a quick read, but prove or sufficiently motivate important statements. And it should cover the essentials needed in introductory theoretical particle physics; i.e. basic representation theory, basic Lie theory, and something about $SU(2)$ and $SU(3)$. Are there any good alternatives?
Comprehensive book on group theory for physicists? I am looking for a good source on group theory aimed at physicists. I'd prefer one with a good general introduction to group theory, not just focusing on Lie groups or crystal groups but one that covers "all" the basics, and then, in addition, talks about the specific subjects of group theory relevant to physicists, i.e. also some stuff on representations etc.  Is Wigner's text a good way to start? I guess it's a "classic", but I fear that its notation might be a bit outdated?
Proving a function is constant, under certain conditions? The problem:  Assume $f: \mathbb{R} \rightarrow \mathbb{R}$ satisfies $|f(t) - f(x)| \leq |t - x|^2$ for all $t, x$. Prove $f$ is constant.  I believe I have some intuition about why this is the case; i.e. if $t$ and $x$ are very close, ($|t - x| = \epsilon$), then $\sqrt{\epsilon}$ will converge to 0, so $|f(t) - f(x)|$ will also converge to zero if you keep taking $t$ and $x$ closer and closer to each other. However, how do I formalize this argument? Thanks. Deleting comments under posts in the mod queue should be easier Ever since mods gained the ability to undelete comments, deleting them has become easier as the confirmation dialog was removed.  However, this is not the case in the mod queue &mdash; I still get a confirmation dialog for each comment I want to delete in the queue under a custom-flagged post (single-comment flags can be deleted just fine). And since this is the place from where I delete comments the most, it can be annoying.  In addition, the "purge comments" button, when invoked from the queue, refreshes it, so I have to scroll back down, remember which post I just purged, and mark the flag as helpful. Usually not a big issue but if there are multiple "obsolete comments" flags, then it can get confusing.  Could the workflow for comment thread moderation from within the queue be improved? Ideally, make comment deletion work like everywhere else on the site, and make the purge button AJAX-based like the comment deletes. Upgrade OpenSSH 7.4 to later on RHEL I have a Red Hat Enterprise Linux server (7.5 x86_64). I have OpenSSH version 7.4. I was asked to upgrade it to a later version for security reasons: Nessus states that . However the Red Hat software and downloads does not have the latest package RPM.  I found some clues on where to get the latest package for OpenSSH. I found , however, I do not know on how to upgrade it and trust this website. I do not want the SSH and other configuration to be modified by the ugrade.  I did find links but however they are not useful, for example .  I would like to know how to upgrade OpenSSH without using yum. According to the original paper of , there is no key validation needed when using Curve25519 for Diffie-Hellman Key Exchange. However, where does this property come from? Is there any proof or argumentation available in order to understand this really practical property of Curve25519? Does this mean that each $x$ coordinate could belong to a point $P=(x,y)$ from Curve25519? Is that even possible? Why is electric field lines away from (+) and toward (-)? I have a questions about the electric field lines.   Well in the basic learning, we know that:   The electric field lines extend away from a positive charge They move forward a negative charge   Let's take parallel plates, which make a uniform electric field.If we take the basic learning, which I mentioned, in accounts, it's very easy to understand that this is the direction of a positive charge object if we put the object between the plate (move away the positive charged plate and toward negatively charged plate).  The problem is if we put a negative charged object between. Isn't the electric field reversed ? Exact Sequences of Modules and Rank Suppose that:  $0 \rightarrow M_{1} \rightarrow M \rightarrow M_{2} \rightarrow 0$  Is an exact sequence of $R$-modules (for $R$ commutative integral domain). Show that $\mathrm{rk}(M) = \mathrm{rk}(M_{1})+\mathrm{rk}(M_{2})$    I have shown the inequality $\mathrm{rk}(M) \geq \mathrm{rk}(M_{1})+\mathrm{rk}(M_{2})$, however for the opposite direction I'm lost. I tried to take $N$ as a linear independent subset and tried to decompose it into $N_{1}$ (the elements in $\mathrm{Ker}(g)$) and $N_{2}$ (the elements not in $\mathrm{Ker}(g)$), but I haven't got far, since $N_{1}$ gives us a linearly independent set in $M_{1}$, however $N_{2}$ can give us a linearly dependent set in $M_{2}$.   We define $\mathrm{rk}(M)$ in this case as the supremum over all cardinalities of the linearly independent subsets of $M$ (where the only finite linear combination equaling $0$ implies trivial coefficients for $r \in R$).  Would this be the proper way to show the result? I think I'm missing something important. Proving by induction that $ \sum_{k=0}^n{n \choose k} = 2^n$ How can I create an AddIn to ArcGIS Pro and where can I find it from ArcGIS Pro application? I came to this conclusion: the primes that can't be written as the sum of two squares (lets use$p\prime$ to denote) can be written as ${p}\prime \equiv 3 \;(\bmod\; 4)$.  I need a simple proof to show this and am stuck. I would appreciate guidance! Say i have this PHP code:  $FooBar = "a string";   i then need a function like this:  print_var_name($FooBar);   which prints:  FooBar   Any Ideas how to achieve this? Is this even possible in PHP? Good reasons to prohibit inheritance in Java? What are good reasons to prohibit inheritance in Java, for example by using final classes or classes using a single, private parameterless constructor? What are good reasons of making a method final? How can I separate a single object file into multiple objects based on closed geometry? Let's say you have a single obj with a number of separate closed 3D geometries in it. For example's sake, imagine you have an obj called neighborhoodfirehydrants.obj that includes the model for all of the fire hydrants on a street, which themselves are closed, but as I said above, are all within the same obj file.  Now let's say you wanted to be able to process each of those fire hydrants one at a time, separately. To the user, it's very obvious to see visually that these faces can be subgrouped into separate "objects" but in the Blender world, it sees them all as one.  I'm looking for a way (script would be ideal) to iterate through a blender obj neighborhoodfirehydrants.obj and find each of the "objects" (fire hydrants) that make it up. I've been looking into using the looping tools, but that's not making sense in this context. A sequence $\{x_j\}$ is said to be fast-Cauchy if $\sum_1^\infty d(x_j,x_{j+1})&lt;+\infty$. Show that every Cauchy sequence has a fast-Cauchy subsequence.   **My attempt:**Argue by contradiction, suppose there is no such subsequence. Then for any subsequence $\{{x_j}_k\}$,  $\sum_1^\infty d({x_j}_k,{x_j}_{k+1})$ diverges. Vaguely recall from an analysis course, if a series diverges, it doesn't not satisfy the Cauchy criterion. That is to say, there exists $\epsilon&gt;0$ such that for all $k$ and all $p\ge1$, $d({x_j}_{k+1},{x_j}_{k+2})+...+d({x_j}_{k+p}+{x_j}_{k+p+1})\ge\epsilon$.  Then I intuitively think that this is a contradiction, since if the original series is Cauchy, then after a large $N$, since $d(x_m,x_n)$ has to be very small, so that their sum should be smaller than given $\epsilon$, which is a contradiction. But I don't know how I can write down the concrete proof? Is there any way to recover deleted files which may have since been overwritten? Answers in top Network Posts showing incorrect score There is already a question  which is posted around a month ago (which was fixed). My question reports a similar issue of showing inaccurate scores along with another bug.   A couple of answers in the Top Answers in my network profile are showing incorrect score.         As we can see they are showing a score of 10. But as of writing this question, the score of both the answers is 9.  and  both have a score of 9 instead of 10.  Even though the current score is 9, both these answers reached a score of 10 a few months ago and I was awarded  for both.         The vote was removed either when a user was removed or there was an unupvote. As far as I can tell, I don't remember an unupvote notification in the achievement box from these answers. My guess is the votes are removed when user accounts were deleted.   So, I suspect the score of answers in Top Network Posts is not updated either when there is an unupvote or a vote thrown away due to account deletion.   Is this the right reason why score is inaccurate? Can this be fixed? What is the proper way to change the DNS IP? CASE WHEN with GROUP BY I have a table that looks like this (oversimplified case of the actual case to make my point)  CREATE TABLE sales (    id int,    currency VARCHAR(5),    price int    shop_id int );   Now I need to make a query that will give me something like this table, grouping by shops yet giving sum of sales per currency My problem is when I make currency column non aggregate it fails because my query becomes non standard. When I add currency to group by then each currency creates new row, something I don't want. I have run out of option and would appreciate any help or pointer to the right direction.  I use MySQL but would appreciate if I would get the solution that works with more databases (PostGreSQL being at the top of the list after MySQL)  Query that works with undesired results  SELECT   shop_id,           (CASE WHEN currency= "GBP" THEN SUM(price) ELSE 0 END) AS POUND,           (CASE WHEN currency= "USD" THEN SUM(price) ELSE 0 END) AS USDOLLAR GROUP BY shop_id, currency   The data that should be produced by the query  shop_id     |   POUND   |   USDOLLAR     -----------------------------------------     1       |   400     |   300 -----------------------------------------     2       |   250     |   100 -----------------------------------------     3       |   400     |   100 ----------------------------------------- Is there any way to tell Google to use a particular account for all Google services by default? I typically use 2 Google accounts simultaneously in my browser. So whenever I fire up any Google service like Google Maps or YouTube or Google Search, it uses one of the accounts. The problem is that I don't want that account to be used and no matter how many times I switch the account for these services, they seem to default to same account.  Is there any way to tell Google to use a particular account for all Google services by default?    I am not talking about using Google account to sign in to third party websites. I am talking only about Google's own services.  I am using Chrome if anyone is going to suggest client-side solution. Unstable wifi with intel 8260 [8086:24f3] (rev 3a) on Ubuntu 16.04 running on Lenovo P50 Some of the Puella Magi seem to have magical powers related to the wishes that they made. Sayaka has regeneration abilities, and she wished to heal someone. Homura has time manipulation abilities, and she wished to go back in time.  But other magical girls, like Mami and Kyouko, don't appear to have powers related to their respective wishes.  So, is there a connection, or is it only a coincidence for Sayaka and Homura? If it's the former, how do Mami and Kouko's wishes relate to their powers?