Why do we use the group $SU(3)$ and not $SL(3, \mathbb{R})$ for color charge?  As far as I can tell, the $SL(3, \mathbb{R})$ is volume and orientation preserving, by the fact that it has unit determinant, and if I'm not mistaken the only thing that $SU(3)$ adds is that it is inner product conserving?  And now to play devils advocate, does that still matter? Ever since the Klein-Gordon equation we have stopped viewing fields as wave-functions, and the expectation values come from calculating things like  $$&lt; F &gt; = \frac{\int \mathcal{D}\phi F[\phi] e^{i S[\phi]}}{\int \mathcal{D}\phi e^{i S[\phi]}},$$  so wouldn't such differences be divided out?  I've also calculated the structural constants and noticed that the anti-symmetric ones are all identical apart from a sign change in $f_{257}$, although for the symmetric ones there are actually a lot of sign changes.  Also, I kind of struggle to see why $SL(3, \mathbb{R})$ would not be norm conserving, is it possible to show this fairly easily?
What is the motivation for including the compactness and semi-simplicity assumptions on the groups that one gauges to obtain Yang-Mills theories?  I'd think that these hypotheses lead to physically "nice" theories in some way, but I've never, even from a computational perspective. really given these assumptions much thought.
I often see $I(t)\propto |E(t)|^2$. What is the exact form ? Which constants are missing to make this an equality and why are they so often omitted ? “How to Ask Questions in Private Beta” is listed in every site’s help centre When I go to /help/asking on any Stack Exchange site (), there is a link to How to Ask Questions in Private Beta (). It starts with:  Welcome to the private beta for [site] The tone and quality of the questions asked during this temporary private beta are critically important. If the private beta doesn't produce enough high quality expert level questions, it won’t proceed onward to the public beta. To help ensure your site makes it out of private beta, here are some tips:  There is no disclaimer or similar that this is outdated. This may lead to unnecessary confusion. I understand that that it is useful to keep this page in public pages for documentary purposes, as it may be linked in early Meta discussions, but it should:  not be listed in the table of contents (/help/asking) have a disclaimer Does an Enlarge/Reduce spell on a druid affect the beast form if the druid Wild-Shapes? If a druid (multiclassed into sorcerer) casts Enlarge on himself so that he becomes a Large humanoid (approximately twelve feet tall), and he then Wild Shapes in a brown bear, is the brown bear form normal size or doubled in all dimensions? What is the center of $D_{2n}/Z(D_{2n})$ What is the center of $D_{2n}/Z(D_{2n})$. I see that when $n=2^k$ then I have a $p$-group so the center is not trivial. But when $n$ is not power of $2$ how can i know what is the center of this group?. Surely when $n$ is odd then the center is trivial. Using --exclude with the du command This is probably something basic but I'm not able to make it work. I'm trying to use DU to get a total size of files minus certain directories. I need to exclude one specific directory called uploads but not every directory called uploads. For example, my file structure looks a bit like this:  /store   /uploads     /junk_to_ignore     /more_junk_to_ignore   /user_one     /uploads   /user_two   I can run the following command:   du -ch --exclude=uploads*    and it gives me the file size minus all the "uploads" directories. However, in trying to exclude certain directories (and all its sub-directories) I fail. I've tried variations of:  du -ch --exclude=./uploads* du -ch --exclude='/full/path/to/uploads/*'   but can't seem to figure it out. How do I exclude a specific directory? %AX = (%AH + %AL)  So why not %EAX = (%SOME_REGISTER + %AX) for some register %SOME_REGISTER? Is it always possible to find the limit of a function without using  or ?  For example,   $$\lim_{x\to0}\frac{\tan x-x}{x^3}$$  $$\lim_{x\to0}\frac{\sin x-x}{x^3}$$  $$\lim_{x\to0}\frac{\ln(1+x)-x}{x^2}$$  $$\lim_{x\to0}\frac{e^x-x-1}{x^2}$$  $$\lim_{x\to0}\frac{\sin^{-1}x-x}{x^3}$$  $$\lim_{x\to0}\frac{\tan^{-1}x-x}{x^3}$$ On our minecraft server, I've built a Nether portal in my basement. Which connected two-way (tested) to a location in the Nether.    This nether portal took me to an area in the nether which was a small cave. I dug upwards and surfaced close to a Nether Fortress. After clearing the fortress of Blaze spawners, I decided to 'move in'. So I went back to the portal, dismantled it, and reactivated in in a location in the Fortress.    The fortress would be within the same 128m radius I would assume as it's really close to the original place. Literally some steps to the surface, then a ladder up the nearest Nether Fortress bridge support.  Now, taking this portal back to my original doesn't work, I spawn deep underground in an Abandoned Mine Shaft.  I read somewhere that my Nether portal has found a 'better match' and this could be remedied by disabling the 'wrong' portal in the mine shaft.  However, upon multiple attempts, a new nether portal is dynamically created in the same area. See screenie for example. You'll see two 'stacked' portals on the left (from my different attempts at disabling) and then the current active one on the right.    My question is, how can I make sure these portals go to the correct place. Is it a matter of returning the portal to it's original location or am I stuck for returning to the basement? Yield return from a try/catch block I have a very large codebase (read: thousands of modules) that has code shared across numerous projects that all run on different operating systems with different C++ compilers. Needless to say, maintaining the build process can be quite a chore.   There are several places in the codebase where it would clean up the code substantially if only there were a way to make the pre-processor ignore certain #includes if the file didn't exist in the current folder. Does anyone know a way to achieve that?  Presently, we use an #ifdef around the #include in the shared file, with a second project-specific file that #defines whether or not the #include exists in the project. This works, but it's ugly. People often forget to properly update the definitions when they add or remove files from the project. I've contemplated writing a pre-build tool to keep this file up to date, but if there's a platform-independent way to do this with the preprocessor I'd much rather do it that way instead. Any ideas? Prove: $\binom{n}{0}F_0+\binom{n}{1}F_1+\binom{n}{2}F_2+\cdots+\binom{n}{n}F_n=F_{2n}$ Prove: $\binom{n}{0}F_0+\binom{n}{1}F_1+\binom{n}{2}F_2+\cdots+\binom{n}{n}F_n=F_{2n}$;  I was stuck with this question for a while... Help me please!!! Thanks!!! "Any" followed by singular or plural countable nouns? This question has troubled me for ages despite my several attempts of looking it up in dictionaries or usage books. Do we say, "Do you have any ideas" or "Do you have any idea"? I do see an example where "any" means "it doesn't matter who/which/what", therefore "You can borrow any book you like." Also, does it matter between using it in questions and negatives? pkgloader is not finding l3regex What do hollow/filled stars mean in chat? I was on chat in Stack Overflow and noticed that some of the message had grey stars with a black border while others were just black stars. What is the difference between the 2 star types? How to get all possible combinations of a list’s elements? I have a list with 15 numbers in, and I need to write some code that produces all 32,768 combinations of those numbers.   I've found  (by Googling) that apparently does what I'm looking for, but I found the code fairly opaque and am wary of using it. Plus I have a feeling there must be a more elegant solution.  The only thing that occurs to me would be to just loop through the decimal integers 1–32768 and convert those to binary, and use the binary representation as a filter to pick out the appropriate numbers.   Does anyone know of a better way? Using map(), maybe? style=apa causes bibliography to fail Does an unbalanced sample matter when doing logistic regression? Okay, so I think I have a decent enough sample, taking into account the 20:1 rule of thumb: a fairly large sample (N=374) for a total of 7 candidate predictor variables.   My problem is the following: whatever set of predictor variables I use, the classifications never get better than a specificity of 100% and a sensitivity of 0%. However unsatisfactory, this could actually be the best possible result, given the set of candidate predictor variables (from which I can't deviate).   But, I couldn't help but think I could do better, so I noticed that the categories of the dependent variable were quite unevenly balanced, almost 4:1. Could a more balanced subsample improve classifications? When I write something like this:     I am a man that is doing these things.   Is it correct to shorten it like this?     I am a man doing these things.   And does it require commas? Is the 5-foot range of the Help action my range to the ally, the enemy, or both? Package incompatibilites: etoolbox, hyperref, and bm, standalone? I am trying to transition to using the etoolbox package, but seem to have run into some difficulties and they appear related to the hyperref and bm packages which to me seem totally unrelated.  The MWE example compiles since \RemoveEToolbox is defined and shows that there is no apparent problem before etoolbox was used.    Commenting out the \def\RemoveEToolbox{} line produces two problems:   With both the \renewcommand, and the usepackage{hyperref} commented, this results in "Runaway argument? Paragraph ended before \bm@test@token was complete". Including the usepackage{hyperref} (with \renewcommand commented) results in "Undefined control  sequence. \Call@AtVeryEndDocument ...cumentHook \@undefined"   But if uncomment the \renewcommand{\bm}{#1} line (effectively doing without any \bm), then this seems to compile.  I have been using this for a while now and things appeared to have been working fine, but now that I attempt to use etoolbox I seem to run into problems.  \documentclass{standalone} \def\RemoveEToolbox{}% Shows that this works fine without {etoolbox}  \usepackage{amsmath} \usepackage{xcolor} \usepackage{bm}  \ifdefined\RemoveEToolbox     \newcommand*{\iftoggle}[3]{#2}% Default to true value of "if" \else     \usepackage{etoolbox}     \newtoggle{paper}     \toggletrue{paper}      %\renewcommand{\bm}[1]{#1}% Why can't I have a normal \bm with {etoolbox}? \fi  % \usepackage{hyperref}  \begin{document}  This document is intended for  \iftoggle{paper}{paper}{electronic} distribution.  \bm{\textcolor{blue}{Solve $x^2-1=0$}}  \begin{align*}     a &amp;= b\\     \iftoggle{paper}{         c &amp;= d\\     }{}     e &amp;= f\\ \end{align*} \end{document}