Let $\mathscr L (\phi(\mathbf x), \partial \phi(\mathbf x))$ denote the Lagrangian density of field  $\phi(\mathbf x)$. Then then actual value of the field  $\phi(\mathbf x)$ can be computed from the principle of least action. In case of motion of particles, I know that principle of least action comes from Newton's second laws. But why does the principle of least action also hold for classical fields like EM field and gravitational field? Is there any deep reason why it holds for both EM and gravitational field?
It is an usual practice that any quantum field theory starts with a suitable Lagrangian density. It has been proved enormously successful. I understand, it automatically ensures valuable symmetries of physics to be preserved. But nevertheless the question about the generality of this approach keeps coming to my mind. My question is how one can be sure that this approach has to be always right and fruitful. Isn't it possible, at least from the mathematical point of view that a future theory of physics does not subscribe to this approach?
Counting traversed arcs on routes to write attributes using ArcGIS for Desktop? I have number of persons located on a road network and I have calculated their shortest distance to a particular location.  From the routes output created from Closest Facility can I   break the routes down into the individual arcs traversed by each person? assign each arc a count attribute indicating the number of individuals who use that arc to get to their destination?   I am using Network Analyst in ArcGIS 10.2 for Desktop. How do I install a different Python version using apt-get? How can I install a different version of Python using apt-get?  Obviously I realise I can install using the source tar ball, however I would prefer not to install from source and instead use the package manager, as that's what it's there for. Surely somewhere reputable builds .deb files for the latest Python releases (why python.org don't is beyond me) that I can reference.   What do I need to do to reference them and what issues might it create when upgrading to the next version?  If there is no way except for building from source, is there a (pseudo) package that I can can install that will provide all of the dependencies needed without having to find and install each individually? So that I don't get:  The necessary bits to build these optional modules were not found: _bz2                  _curses               _curses_panel       _dbm                  _gdbm                 _lzma               _sqlite3              _ssl                  _tkinter            readline              zlib Is it possible to install Office 365 (2013) on Ubuntu 15.04 Vivid Vervet? I would like to install Office 2015/365 on Ubuntu 15.04. I tried to install Office using Wine, but that did not work. Please note that I do not want virtualisation unless it has a -like behaviour, where application windows are treated like regular Ubuntu application windows by the system. Galois extension is (not) transitive Let $ K/ L /F $ be fields. If $K / L$ is Galois and $ L / F $ is Galois, then $ K / F$ is Galois. We mentioned this very quickly in today's class without justifying. But I have trouble seeing this. Any help is appreciated.  Our definition for $ K / F$ being Galois is the $F$-automorphism group $G = G( K / F) : = \{ \sigma \in aut (G) : \sigma_F = id_F \}$ fixes only $F$, i.e. $ \{ x \in K : \sigma (x) = x \text { for all } \sigma \in G  \} = F$.  But we also showed that $ K /F$ is Galois if and only if $ K/F$ is normal and separable. Words that mean ''to say something unintentional'' I am looking for words that mean ''to say something unintentionally'' Can't create new folder from anywhere in Windows 7 I have this problem on two of my new laptops and can't seem to find a decent workable solution elsewhere in forum land. The problem is that on my Windows 7 Professional machines the right mouse button doesn't show the New Folder option and elsewhere as well (via Explorer) I'm unable to create new folders.   I'll be happy to get this tiny problem resolved and declare that Windows 7 is almost perfect! Thanks to all of you in advance for your contribution!  PS: None of the Vista solutions seem to work here!      Tried NewFolderFix.reg, didn't work - "Not all data was succesfully written to the registry. Some keys are open by the system or other processes."  Converted FolderFix.reg to .inf file and that worked.  Don't recall the problem appearing after an update.  MS answer to the explore process hanging (KB 972685) was to install the latest Visual C++ Update (vcredist.exe).  Nope. That didn't help either.  I haven't touched Silverlight since installation when Windows 7 hit the shelves. I tortured the RC installation before that, and never had problems there either.    UPDATE-  Logged back into Administrator account, still missing from there. Spent a bit more time looking instead of just fixing. Just yto make sure, logged back into my user account - still OK there.  Turns out the entries in HKCR\CLSID were the culprit here. Reg file wouldn't take again (as above) but inf file fixed it. This key was unable to be entered from regfile, or altered or deleted in Regedit (Permissions).   Don't quite understand why a common key in HKCR needed to be entered separately for each user.   Here is the file I used to fix it. Just copy into notepad, save as newfolderfix.inf, rt-click and select Install  ================================================================  [Version]  Signature=$Windows NT$  [DefaultInstall]  AddReg     =REGEntries.AddReg  [REGEntries.AddReg]  HKCR,"%String0%",,0x0,"CLSID_ExecuteFolder"  HKCR,"%String0%\InProcServer32",,0x0,"ExplorerFrame.dll"  HKCR,"%String0%\InProcServer32","ThreadingModel",0x0,"Apartment"   [Strings]  String0 = "CLSID\{11dbb47c-a525-400b-9e80-a54615a090c0}"  =============================================================   Thanks to others who helped point me in the right direction. I have two laptops (same manufacture), with the same type of power connector.  However, the power supplies/transformers are slightly different.    The output on the first laptop's power supply is 15.6&nbsp;V at 8.0&nbsp;A. The output on the second laptop's power supply is 15.6&nbsp;V at 5&nbsp;A.  Clearly the voltages are the same, but the currents are different. I assume the second laptop's power supply can not be used on the first, because it can't supply enough power to the laptop.   However, can the first laptop's power supply be safely used on the second laptop? Why is the laboratory frame energy always greater than the center of mass frame energy? I have been looking for an answer to 'Why is the laboratory frame energy always greater than the center of mass frame energy during collisions?'.  A lot of resources provided mathematical explanations. I wanted to get some perspectives in terms of physics.  Could you explain this? What is the difference between a predicate and function? I need to to understand the difference between predicates and functions in the context of Clasual Form Logic in order to define the Herbrand universe.  If I have p(x) :- q(f(x)) would I be right in saying that p and q are predicates while f is a function because it is "nested"?  By this thinking then if I have p(x) :- q(x) both p and q are predicates and I have no functions?  If this is incorrect then how can I tell the difference between a predicate and function? Accoring to Joseph Wright's answer at   The k-type argument has recently been adjusted: you now want e-type  Questions:  What is the functionality of the new e-type argument and how does it differ from the previous k-type argument?  The 2016-11-21 version of the xparse documentation does not mention the k-type argument at all. Is the plan to leave the earlier k functionality intact (but deprecated so no documentation) or will it eventually be removed and any usage of that should eliminated? If the plan is for it to be removed, how long will the older k-type argument functionality be kept in xparse.   Code: Example of the k-type argument from . Would be useful to see how this would be modified to use the new e-type argument. \documentclass{article}  \usepackage{amsmath} \usepackage{xparse} \usepackage{xcolor}  \NewDocumentCommand\MyMacro{k_}{%     \IfNoValueTF{#1}{%         \mathbf{A}     }{%         A_{\textcolor{red}{#1}}     }% }  \begin{document}  With a subscript: $\MyMacro_{\pi}$   Without any subscript: $\MyMacro$   \end{document} Is there any way to include an animated GIF directly? Is there any way to include an animated GIF directly in either PDFLaTeX or XeLaTeX? I realize the animate package can include animations in a PDF, but it doesn't support animated GIFs and you have to split them up manually into EPS or PNG files as far as I can tell. How to add item to right-click menu when NOT selecting a folder or file? How do I add a menu item to my context menu to open up powershell (or any other arbitary application) when I right-click inside Windows Explorer?  I found tons of links on how to add menu items when doing this: (selecting a folder; )    ...but couldn't find any instructions on how to add menu items when doing this: (not selecting a folder or file)    I did find  and tried adding powershell to HKEY_CLASSES_ROOT\Directory\Background\shell\, (loosely based on the  and linked above) but it didn't work for me.  I'm running Windows 7, by the way.  Also, I'm currently interested in adding only PowerShell, but I'd prefer a general solution I can apply to add any program to the context menu. Proving the measure of an increasing sequence of measurable sets is the limit of the measures When I visit a site I haven't visited (while logged in) for a while, I see:  Welcome back! If you found this question useful, don't forget to vote both the question and the answers up.  That's often intended behavior. But today I visited  and was shown that banner even though the question and all its answers are locked. Voting arrows aren't even shown on any of the posts on that page. I believe that banner should be disabled on pages where there is no post that can be voted on by anyone. No analytic function in $\{|z|<1\}$ such that $f(0)=1$ and $|f(z)|\ge 1+|z|^2$. Proof strategy Show there is no analytic function in $\{|z|&lt;1\}$ such that $f(0)=1$ and $|f(z)|\ge 1+|z|^2$. I guess something went wrong along the way and I would like your assistance.   $f$ does'nt get a maximum in the domain, because if it did, it would be constant in the domain, meaning $|f(z)|=1\ge 1+|z|^2$ which doesn't hold for all z. Since $f$ isn't zero in the domain, ${1\over f}$ is analytic in the domain. but $|{1\over f(z)}|\le {1\over 1+|z|^2}\le 1={1\over f(0)}$, which indicates a local maximum making ${1\over f}$ constant, contradiction the fact the $f$ isn't. What am I really lacking here? MacBook Pro never goes to sleep Angle between 2 points Given the following image:   $\hskip{1.5 in}$   Supposing $A(100, 300)$ and $B(300, 100)$, how can I find the angle $\alpha$ between A and B?  On a side note, what's the main difference between a point and a vector? translating a point to a vector is as simple as Point = Vector? Sometimes I find articles where the terms are interchangable Every power series is the Taylor series of some $C^{\infty}$ function This option, which was present in the "Mouse and Touchpad" settings panel in previous versions, is for some reason absent in 16.04 LTS. Does anyone know why this is, and/or how to fix it? Thanks. I have a .tiff and a .tfw file that I want to change into a GeoTIFF. When I try to open the file in ArcMap and ENVI 5.0, it is successful. However, in Google Earth it is not.  Is there anyway to create the GeoTiff in ArcMap or ENVI?