I want to understand the relationship of the so common $SU(N)$ and $SO(N)$ groups in physics with the symplectic group which I think is the double cover of the first and the Spin groups $Spin(N)$.  Is there a good reference, mainly 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 I guess it's a "classic", but I fear that its notation might be a bit outdated?
QGIS query syntax differs between attribute table and feature filter Using QGIS 2.16.2, I can successfully select records from a shapefile attribute table using the following expression:  left("start_time", 10) = '2015-08-01'   Please note that start_time is a string field.  However, when I copy and paste the same expression into the shapefile's Layer Properties>General>feature filter>Query Builder I get the following error:    I would expect that the same expression would work everywhere in QGIS.  What am I doing wrong? With biblatex, the author can be replaced by a dash (or “idem”) in the bibliography. Is it possible to have this replacement also if there are multiple authors, and the first of these multiple authors is the same as the author of the book listed before? (It is somewhat difficult to describe, see the attached example instead, where “Buchautor, Hans-Wilhelm” should be replaced in book3 as well.)   I assume that it should be possible by customising \DeclareNameFormat, but I don’t know how.  Minimal example:  \documentclass{scrartcl} \usepackage[T1]{fontenc} \usepackage[latin1]{inputenc} \usepackage[english]{babel} \usepackage{csquotes} \usepackage{filecontents} \begin{filecontents}{\jobname.bib} @BOOK{book1,   author = {Buchautor, Hans-Wilhelm},   title = {Irgendein Buch},   location = {Buch am Wald},   date = {2000} } @BOOK{book2,   author = {Buchautor, Hans-Wilhelm},   title = {Ein anderes Buch},   location = {Berlin},   date = {2001} } @BOOK{book3,   author = {Buchautor, Hans-Wilhelm and Zweitautor, Zoran},   title = {Noch ein Buch},   location = {London and New York},   date = {2010} } \end{filecontents}  \usepackage[ style=authortitle, backend=bibtex8 ]{biblatex} \bibliography{\jobname}  \renewcommand*{\bibnamedash}{%   \bibstring[\mkbibbold]{idem\thefield{gender}}}  \begin{document} \nocite{*}  \printbibliography \end{document}   Edit 15/02/2011 17:14   I should have added that there was a feature request for biber which pointed back to biblatex. See .  Edit 21/06/2011 9:26  Is this somehow possible now with biblatex 1.4/1.5? I played a bit with uniquename/uniquelist, but I could not get it to work. How to permanently turn off online results I don't like getting online results when searching in my dashboard, so I went to System Settings &gt; Security &amp; Privacy &gt; Search, and I turned the setting off:    But when I restart my machine, the setting is always reset to:    So how can I permanently disable it without it turning on again after a restart?  Information Update:  I have had a look at the post that this has been marked as a possible duplicate of, and I don't think that my question really is a duplicate of it, as the other question is asking about how to set it globally, and I am not, I am only wanting to set it for one user, so the fact that it is not global is not the problem, the problem is that it is not sticking for that one user, and just resetting to its default state after a restart. In fact, I don't want it to be set globally, and the answers from the other question only really explain how to do that.    OS Information:  Description:    Ubuntu 15.04 Release:    15.04   Package Information:  unity:   Installed: 7.3.2+15.04.20150420-0ubuntu1   Candidate: 7.3.2+15.04.20150420-0ubuntu1   Version table:  *** 7.3.2+15.04.20150420-0ubuntu1 0         500 http://gb.archive.ubuntu.com/ubuntu/ vivid/main amd64 Packages         100 /var/lib/dpkg/status Find $\sum\limits_{k\, \text{ odd}} \frac{2(k^2-1)}{k^4+k^2+1}$ Table of Contents for poetry collection (ConTeXt) I'm getting stumped about how to generate the ToC for this book. I'm about to give up and just do it by hand. The author wants to include a lot of structural information that isn't present in the actual text, and none of the numbers "roll over" as they're want to do in ConTeXt.  This is the desired effect:    Narrator 1...      FIRST PART: PART SUBTITLE  1). First Poem // First Poem (Spanish title) . . . . . . . . . . . . . . . . .    1     Author of Poem (b. XXXX d. XXYY)  2). Second Poem // Poema Secunda . . . . . . . . . . . . . . . . . . . . . . .    3     Author of Poem    Narrator 2...  3). Third Poem // Third Poem . . . . . . . . . . . . . . . . . . . . . . . . .    5     Author      SECOND PART: Part 2  4). Fourth Poem // Fourth Poem . . . . . . . . . . . . . . . . . . . . . . . .    7     Author    Narrator 3...   The problems I have essentially boil down to these:   There is this weird "narrator" concept that doesn't seem to contain or be contained by the part/poem structure. A new part doesn't imply a new "narrator" and a new "narrator" doesn't imply a new part. I need to aggrandize each title with the title in translation and the author, and I want to typeset them nicely. I need poems to continue counting up across parts.   I see basically three approaches:   Make each poem a chapter and customize the appearance with \setuphead[chapter][....]. Then use \writebetweenlist[chapter] to add the Narrator and author information. Make a new list with \definelist[poem] and \definecombinedlist[content][part,poem]; continue using \writebetweenlist[poem] to insert the author and Narrator. This feels like the most conceptually valid option, but I think I'll still need a lot of customization. Forget all about ConTeXt and switch to plain TeX, use eplain's writetocentry system. Make it look right and forget maintainability. My Command is below and its print Free CPU and Used CPU below format.  I want to restrict awk output to 2 decimal place.  grep 'cpu ' /proc/stat | awk '{usage=($2+$4)*100/($2+$4+$5)} {free=($5)*100/($2+$3+$4+$5)} END {print "Used Cpu:",usage "%"} {print "Free Cpu:",free "%"}'   Output :   Free Cpu: 98.9588%  Used Cpu: 1.04125%   Desired output :  Free Cpu: 98.95%  Used Cpu: 1.04% What order should Asimov's Foundation series be read in? copy and paste doesn't work in terminal Can I change the color of the last selected face? Can I change the color of the last selected face, so that it is the same as the other selected faces?  Here, I've selected the left face then the right face. Note the right face is some sort of checkered or dithered pattern, and just the outline has the nice orange 'selected' color.    Here I've selected the top face, note the right face has now the nice color.    And here I've deselected the top face. Now, both of the remaining selected faces have the nice color. This is the result I'd rather see instead of image 1. What are the different widely used RAID levels and when should I consider them? This is a  about RAID levels.    What are:   the RAID levels typically used (including the RAID-Z family)?  deployments are they commonly found in? benefits and pitfalls of each? Turn off text message (SMS) sync to Exchange email account I recently started using a Samsung Galaxy S4 and one of the features in a synchronization between text messages and email accounts.  When a text message comes in it throws a copy into my Exchange email accounts that are one the phone. I want to turn this feature off but cannot find a setting for it anywhere.  Any ideas? Is there a way to convert number words to Integers? Proving $\sum_{k=1}^n\frac1{\sqrt k}<2\sqrt n$ by induction I am just starting out learning mathematical induction and I got this homework question to prove with induction but I am not managing. $$\sum_{k=1}^n\frac1{\sqrt k}&lt;2\sqrt n$$ Please help! How can I classify data with the nearest-neighbor algorithm using Python? Limiting double to 3 decimal places Q. Find all pairs $(p,n)$ of positive integers where $p$ is prime and $p^3-p=n^7-n^3$.   Rewriting the given equation as $p(p+1)(p-1)=n^3(n^2+1)(n+1)(n-1)$, we see that $p$ must divide one of the factors $n,n+1,n-1,n^2+1$ on the $\text{r.h.s}$.   Now, the $\text{l.h.s}$ is an increasing function of $p$ for $p\ge1$. This implies that for any given $n\ge1$, there is exactly one real $p$ for which $\text{l.h.s}=\text{r.h.s}$. For $p=n^2$, we get $\text{l.h.s}=n^6-n^2&lt;n^7-n^3=\text{r.h.s}.$ This means that either $p&gt;n^2$ or $p&lt;n^2$ must hold.  Assuming $p&gt;n^2$, it follows that the prime $p$ cannot divide any of $n,n+1,n-1$. So $p$ must divide $n^2+1$ and hence $p=n^2+1\quad (\because p&gt;n^2)$.  Substituting the value of $p$ in the given equation we get, $n^2+2=n^3-n\implies n^3-n^2-n=2$. As the factor $n$ on the $\text{l.h.s}$ must divide $2$, the above equation has a unique integer solution $n=2$.  Finally, we get $(5,2)$ as the solution to the given equation.      But how do I conclude this is the only solution possible? Also, why does'nt $p&lt;n^2$ (the case which I ignored) hold? As a bonus question, I would like to ask for any alternative/elegant solution (possibly using congruence relations) to the problem. What are the norms in Ito isometry? Itō isometry from :     Let $W : [0, T] \times \Omega \to \mathbb{R}$ denote the canonical   real-valued Wiener process defined up to time $T &gt; 0$, and let $X :  [0, T] \times \Omega \to \mathbb{R}$ be a stochastic process that is   adapted to the natural filtration $\mathcal{F}_{*}^{W}$ of the Wiener   process. Then $$      \mathbb{E} \left[ \left( \int_{0}^{T} X_{t} \, \mathrm{d} W_{t} \right)^{2} \right] = \mathbb{E} \left[ \int_{0}^{T} X_{t}^{2} \,  \mathrm{d} t \right], $$ where $\mathbb{E}$ denotes expectation with   respect to  $\gamma$. In other words, the Itō   stochastic integral, as a function, is an isometry of normed vector   spaces with respect to the norms induced by the inner products $$      ( X, Y )_{L^{2} (W)} := \mathbb{E} \left( \int_{0}^{T} X_{t} \, \mathrm{d} W_{t} \int_{0}^{T} Y_{t} \, \mathrm{d} W_{t} \right) =  \int_{\Omega} \left( \int_{0}^{T} X_{t} \, \mathrm{d} W_{t}  \int_{0}^{T} Y_{t} \, \mathrm{d} W_{t} \right) \, \mathrm{d} \gamma  (\omega) $$ and $$      ( A, B )_{L^{2} (\Omega)} := \mathbb{E} ( A B ) = \int_{\Omega} A(\omega) B(\omega) \, \mathrm{d} \gamma (\omega). $$   I was wondering what the two normed spaces are and what their norms are, so that the two normed spaces are isometric wrt their norms?  Thanks and regards! How do I get current date/time on the Windows command line in a suitable format for usage in a file/folder name? BibTeX: Abbreviate first name (aka given name) to 2 or 3 letters (not 1) Find all solutions of the equation $n^m=x^2+py^2$ which satisfy the following properties Prove or disprove that,     There always exists a solution of the equation, $$n^m=x^2+py^2$$ with odd $x$ and $y$ and for all $m\geq k$ for some positive integral $k$. Here $p$ is an odd prime and $n\in 2\mathbb{N}$. Is $k$ dependent on $n$? If so then find a way to calculate the value of $k$.   This is basically one of my conjecture which I am trying to prove for quite sometime. Unfortunately, I have progressed very little in this problem. So far I have been only able to prove that for all $m\geq3$ , $n=2$ and $p=7$ there is always a solution of the equation meeting the constraints.   Any idea how to tackle the problem?    Update  After D. Burde's answer of the original problem (see below) I am now interested in finding all $(n,m,p)$ triplets such that the equation holds. Any ideas regarding this problem?