I have read Srednicki's Quantum Field Theory book. I want to learn more about advanced topics in field theory, such as geometry and topology in field theory, topology defect, anomaly, soliton, instanton, renormalization，advanced application in condensed matter physics and so on. Does anyone have anything recommended? Thanks
There's a fairly standard two or three-semester curriculum for introductory quantum field theory, which covers topics such as:   classical field theory background canonical quantization, path integrals the Dirac field quantum electrodynamics computing $S$-matrix elements in perturbation theory, decay rates, cross sections renormalization at one loop Yang-Mills theory spontaneous symmetry breaking the Standard Model   What is a good, complete and comprehensive book that covers topics such as these?
No sound from speakers on MacBook Pro except the startup chime After plugging my headphones out, suddenly there is no sound from the internal speakers. When I press volume buttons, I see a circle-backslash symbol below the speaker icon.  Restarting doesn't help. However I do hear the startup chime. What should I do? Extrude Faces along Local Normals I am trying to extrude faces of a cylinder along local normals. 3dsmax can do it easy, couldn't find how to do it in blender.  The extrude region option extrudes it as shown in the first example. I want it done like the 2nd example. How does JavaScript .prototype work? I'm not that into dynamic programming languages but I've written my fair share of JavaScript code. I never really got my head around this prototype-based programming, does any one know how this works? var obj = new Object(); obj.prototype.test = function() { alert('Hello?'); }; var obj2 = new obj(); obj2.test();  I remember a lot discussion I had with people a while back (I'm not exactly sure what I'm doing) but as I understand it, there's no concept of a class. It's just an object, and instances of those objects are clones of the original, right? But what is the exact purpose of this &quot;.prototype&quot; property in JavaScript? How does it relate to instantiating objects? Update: correct way var obj = new Object(); // not a functional object obj.prototype.test = function() { alert('Hello?'); }; // this is wrong!  function MyObject() {} // a first class functional object MyObject.prototype.test = function() { alert('OK'); } // OK  Also these  really helped a lot. Computation of likelihood when $n$ is very large, so likelihood gets very small? In summer, should I close curtains during the day? Can we create a subsection of the References Cited section with different reference numbering? What is a "good fit" Brier score and Harrell's C Index Four complex numbers $z_1,z_2,z_3,z_4$ lie on a generalized circle if and only if they have a real cross ratio $[z_1,z_2,z_3,z_4]\in\mathbb{R}$ Let $[z_1,z_2,z_3,z_4]$ denote the  of the complex numbers $z_1,z_2,z_3,z_4\in \mathbb{C}$. Show that the distinct points $z_1,z_2,z_3,z_4\in\widehat{\mathbb{C}}$ lie on a generalized circle if and only if $[z_1,z_2,z_3,z_4]\in\mathbb{R}$.    I saw this statement claimed in , and wondered how one would go about showing it. I know of some facts we could work with:   First, the definition: A  in $\mathbb{C}$ is either a circle or a line in $\mathbb{C}$. I know that a Mobius transformation maps generalized circles to generalized circles. I know that if $f$ is a Mobius transformation and $z_j'=f(z_j)$, $j=1,2,3,4$, then $[z_1',z_2',z_3',z_4']=[z_1,z_2,z_3,z_4]$.   I have posted a potential proof as an answer below. Please let me know if you think it's complete. Thank you! I can always find that in some articles the production of higgs decay written as &quot;$\rm H\to {ZZ}^*\to 4l$&quot;, &quot;$\rm H\to ZZ\to 4l$&quot;, &quot;$\rm H\to Z\gamma^*\to\ldots$” What dose it mean when some particles with a superscript *? Such as “$\rm Z^*, W^*, \gamma^*, \ldots$&quot;. What’s the difference between them and &quot;$\rm Z, W, \gamma$&quot;? Splicing a list of arguments into a function with Sequence How to test for an hold item name in Minecraft? I'm trying to make a command block that spawns an item in front of you if you are holding an item with a specific name. I've got these two working scripts;  /testfor @p[r=10] {Inventory:[{tag:{display:{Name:"Item Name"}}}]}  /testfor @p[r=10] {SelectedItemSlot:0,Inventory:[{Slot:0b,­id:"minecraft:diamond_sword"}]­}   but I can't get them together. The block should only look for an item in the active slot. See code:   var file1 = "50.xsl"; var file2 = "30.doc"; getFileExtension(file1); //returns xsl getFileExtension(file2); //returns doc  function getFileExtension(filename) {     /*TODO*/ } Added activities, now names and labels and strings aren't registering Android Manifest file Preservation of ideals in localized rings Refer to localization of rings in Lang's Algebra p. 108. In particular, let $A$ be a commutative ring, $S$ a subset of $A$ that is a submonoid of the multiplicative monoid structure of $A$, containing the identity. Then  $S^{-1}A$ is the set of elements $\frac{a}{s}$ with $a \in A$ and $s \in S$.  We have $\frac{a_1}{s_1}=\frac{a_2}{s_2}$ if there exists $\bar{s} \in S$ such that $\bar{s}(s_2a_1 - s_1 a_2)=0$. Now consider the injection of $A$ into $S^{-1}A$ given by $x \mapsto \frac{x}{1}$. This is a ring homomorphism. Let $J$ be an ideal of $A$. Ring homomorphisms preserve ideals and so the injection of $J$ into $S^{-1}A$, call it $J^{*}$, will be an ideal. My problem is that i don't see why for any $\frac{a}{s} \in S^{-1}A$ and any $\frac{j}{1} \in J^{*}$ we will have that $\frac{aj}{s}$ will be in $J^{*}$, i.e. why there must exist an element $\kappa \in J$ such that $\frac{aj}{s}=\frac{\kappa}{1}$. When should I use "a" vs "an"? In the following example, is it appropriate to use a or an as the indefinite article, and why?     He ate __ green apple.   I know that in the case of just "apple", it would be "an apple," but I've heard conflicting answers for "green apple," where the noun is separated from the article by an adjective.  Also, which is more appropriate in this case:     He ate  __ enormous Pop-Tart. Running JAR file on Windows I have a JAR file named helloworld.jar. In order to run it, I'm executing the following command in a command-line window:  java -jar helloworld.jar   This works fine, but how do I execute it with double-click instead? Do I need to install any software? Implicit newline at the end of each paragraph? How to install the previous version of a .deb package and pin it? I am trying to install the latest version of subversion on Sid, and because it has a bug I receive a warning and I abort the installation. How do I get to locate the previous version version, install it and pin until the bug is resolved?  root@server01:~# apt-get install subversion   Reading package lists... Done                                                                                                                                                                                  Building dependency tree                                                                                                                                                                                       Reading state information... Done                                                                                                                                                                              Suggested packages:                                                                                                                                                                                              db5.3-util subversion-tools                                                                                                                                                                                  The following NEW packages will be installed:                                                                                                                                                                    subversion                                                                                                                                                                                                   0 upgraded, 1 newly installed, 0 to remove and 205 not upgraded.                                                                                                                                               Need to get 0 B/981 kB of archives.                                                                                                                                                                            After this operation, 4,844 kB of additional disk space will be used.                                                                                                                                          Retrieving bug reports... Done                                                                                                                                                                                 Parsing Found/Fixed information... Done                                                                                                                                                                        critical bugs of subversion (-&gt; 1.9.2-2) &lt;Outstanding&gt;                                                                                                                                                          b1 - #803725 - subversion: dump-load of a repository modifies verbose log output: M line lost serious bugs of subversion (-&gt; 1.9.2-2) &lt;Outstanding&gt;  b2 - #803589 - FTBFS with ruby2.2 (only) Summary:  subversion(2 bugs) Are you sure you want to install/upgrade the above packages? [Y/n/?/...] n ********************************************************************** ****** Exiting with an error in order to stop the installation. ****** ********************************************************************** E: Sub-process /usr/sbin/apt-listbugs apt returned an error code (10) E: Failure running script /usr/sbin/apt-listbugs apt Why there is "the" before some names but not others Is there a rule beyond the common "no the with proper nouns and names" for the following problem?     I saw the Empire State Building.      We went to the White House.      We saw the Golden Gate Bridge.   but     I went to Death Valley National Park.      I crossed Brooklyn Bridge. Is there a "smallest" divergent sum?