The  says that a body moves in such a way that the action value $S=\int L dt$ is stationary (often minimal). The principle is written as $$\delta S =0 \ .$$ In contrast,  between an in and an out state is $$ \langle{\rm out}| \delta S |{\rm in}\rangle = \frac{\hbar}{i}  \delta \langle {\rm out}|{\rm in}\rangle \ .$$ I have a simple question: what is minimized in this case? Or, more generally: what does the principle state, if only words are used? That would be my question 1. Question 2. Least action implies that the actual trajectory is special: it differs from all the others, because it has minimal/stationary action. In what sense does Schwinger's principle make the actual state evolution special from all the others? Answering a similar, older , Qmechanic had written:  Schwinger's quantum action principle is not a variational principle in the sense of finding stationary points for a functional. Rather it gives a formula for how a quantum system (typically an overlap/transition amplitude ⟨𝐴|𝐵⟩) changes under a change of external parameters/sources in the action 𝑆.  Can one add a few sentences to complete the answer to question 2? In what sense is the quantum motion special? How does it apply to free particles? Or: how can one express the quantum action principle for free particles in words? Question 3. How does Schwinger's action principle become the least action principle in the classical limit? Ok, if $\hbar$ is zero, the two equations are very similar. Is that the way the transition is made? What can be said to make it clearer? Question 4. The right hand side of Schwinger's principle is $-i\hbar$ times a complex number with a magnitude equal or smaller than one. Why does it enter the principle? Is it correct to say that for long times, the overlap is small, and thus the right hand side is zero?
At the moment I'm working with the . For this I read the following paper: .  But I have some mathematical problems with this formalism. I don't really see why this is a variation principle since it is opartor-valued.   The action principle is defined by: $\delta S  = G_1 -G_2$, where $S$ is the action operator $S = \int_{t_1}^{t_2} dt ~L$ and $G$ the generator operators of the transformations.  What does it mean that the action principle is operator-valued? For the classical action where $S$ is real we search for a stationary point but for operators? I also have a problem that $\delta S \neq 0$. What interpretation has this additional term $G_1 - G_2$?
How do I turn on workspaces? (Why do I only have one workspace?) It appears that Unity on Raring only comes with a single virtual desktop (aka workspaces) by default, and CCSM's Wall plugin has no way to add more. Is this configurable at all? Which is more formal: "My parents will reside with me and my family" or "my family and I"? Why are eigenfunctions which correspond to discrete/continuous eigenvalue spectra guaranteed to be normalizable/non-normalizable? These facts are taken for granted in a QM text I read. The purportedly guaranteed non-normalizability of eigenfunctions which correspond to a continuous eigenvalue spectrum is only partly justified by the author, who merely states that the non-normalizability is linked to the fact that such eigenfunctions do not tend to zero at infinity.  Not a very satisfying answer. What I'm really after is an explanation based in functional analysis. I believe there is a generalized result about inner products being finite for discrete spectra but infinite for continuous spectra.  Can anyone shed some light on this? Microsoft.ACE.OLEDB.12.0 provider is not registered I have a Visual Studio 2008 solution with two projects (a Word-Template project and a VB.Net console application for testing).  Both projects reference a database project which opens a connection to an MS-Access 2007 database file and have references to System.Data.OleDb.  In the database project I have a function which retrieves a data table as follows   private class AdminDatabase    ' stores the connection string which is set in the New() method    dim strAdminConnection as string     public sub New()    ...    adminName = dlgopen.FileName    conAdminDB = New OleDbConnection    conAdminDB.ConnectionString = "Data Source='" + adminName + "';" + _        "Provider=Microsoft.ACE.OLEDB.12.0"     ' store the connection string in strAdminConnection    strAdminConnection = conAdminDB.ConnectionString.ToString()    My.Settings.SetUserOverride("AdminConnectionString", strAdminConnection)    ...    End Sub     ' retrieves data from the database    Public Function getDataTable(ByVal sqlStatement As String) As DataTable         Dim ds As New DataSet         Dim dt As New DataTable         Dim da As New OleDbDataAdapter         Dim localCon As New OleDbConnection           localCon.ConnectionString = strAdminConnection          Using localCon             Dim command As OleDbCommand = localCon.CreateCommand()             command.CommandText = sqlStatement             localCon.Open()             da.SelectCommand = command             da.Fill(dt)             getDataTable = dt         End Using      End Function End Class   When I call this function from my Word 2007 Template project everything works fine; no errors. But when I run it from the console application it throws the following exception     ex = {"The 'Microsoft.ACE.OLEDB.12.0'   provider is not registered on the   local machine."}   Both projects have the same reference and the console application did work when I first wrote it (a while ago) but now it has stopped work.  I must be missing something but I don't know what.  Any ideas? "Show," "shown," and "showed" gzip: stdin: not in gzip format When I run:  tar -zxvf john-1.7.0.2.tar.gz   I get this:  gzip: stdin: not in gzip format tar: Child returned status 1 tar: Error is not recoverable: exiting now   It should start unpacking.  Some people told me not to use the z but I get the same error.  It's a file that I downloaded this way:  wget http://openwall.com/john/f/john-1.7.0.2.tar.gz Parse JSON using Python? Can Cycles use multiple UV layers? I'm trying to match Cycles to a Blender-Internal material setup and I didn't see a way for cycles to have an image reference more then one UV map.  Is it possible to have a node setup with 2 image textures, each using a different mesh UVLayer? In naive set theory, I believe ∅ = {∅} = {{∅}} is correct, but just wanted to make sure that I understood this correctly.   ∅ is an empty set, so having an empty set as an element of a set that contains nothing else is pretty much the same thing as e.g. marking the number 2 as 2.000000, right? Doesn't the symbol ∅ intrinsically imply that this is an empty set which contains it self? How to configure Micromax 352g USB Modem? I want the driver software for my Micromax 352g USB modem for Ubuntu 12.04 LTS. On Ubuntu 10.04 sakis3g was working well, but it is not working on Ubuntu 12.04 LTS. LaTeX template for typesetting a novel I'd like to use LaTeX to typeset a novel. Could you recommend me any template?  What I mean is a template (some .tex file) where I can include my chapterN.tex files (mainly plain text) and get a pretty good design with zero work :) Is there any differences between      Try to do   And     Try doing   Thank you in advence. For $a,b,c,d \in \mathbb{R}$, is $\sqrt{a^2+b^2} + \sqrt{c^2+d^2} \geq \sqrt{(a+c)^2 + (b+d)^2}$? I have tried to show this using the fact that $\sqrt{x+y}\leq\sqrt{x}+\sqrt{y}\; $  for non-negative $x,y$ but haven't been able to arrive at a proof. Display SharePoint Online in an iframe on different domain We would like to display pages from SharePoint Online in an iframe of a Page hosted somewhere else, e.g. in an Azure Web App:  &lt;iframe src="https://site.sharepoint.com/"&gt;&lt;/iframe&gt;   When we do this (in Chrome for example), we get the following error:     Refused to display " ⏎                      Home.aspx" in a frame because it set 'X-Frame-Options' to 'SAMEORIGIN'.   A Page from SharePoint 2013 (on premise) can be displayed in an iframe from a Page hosted on another domain, if the following control is added to the head of the master page:  &lt;WebPartPages:AllowFraming runat="server" /&gt;   However if this control is not added to the master-page, then we also get the above mentioned error.  As far as I know there is no possibility to adjust the master-page in a SharePoint Online Team Site. Is that correct?   In a Publishing Site you are allowed to adjust the master-page, or even add a new one. But I can't find anything similar in Team Sites.  Does anybody know if it is somehow possible to configure domains which do not fall under the "X-FRAME-OPTIONS: SAMEORIGIN"-policy in a SharePoint Online environment? Or if there is another possibility to display SharePoint Online content in an iframe on a different domain. I checked google, checked the Site settings and checked the Office 365 admin center, but didn't find anything. Trying to show that $\ln(x) = \lim_{n\to\infty} n(x^{1/n} -1)$ How do I show that $\ln(x) = \lim_{n\to\infty} n (x^{1/n} - 1)$?  I ran into this identity on . I haven't been able to find any proof online and my efforts to get from $\ln(x) := \int_1^x \frac{\mathrm dt}t$ to that limit have been a failure. How to convert Local time to UTC time in Delphi? and how to convert it back from UTC to local time? how to replace multiple strings together in Oracle Select organic group on the user registration form There's a post already on the post installation forum, but I'm not sure if this is a OG bug.   I am using Drupal 7 and OG 7.x-2.1 version. There is no "Group Audience" in the manage fields page and I think it is replaced with "Group membership", the field type is "Entity Reference" and the widget is "OG Reference". Also there is no input type in the field setting page and I can not find any field that has a "Always show other groups" option. I have checked the option "Show on registration form of that field, but the combo box on the registration form does not have any option. Any suggestion? Enumerate paragraphs and subparagraphs like sections but with letters I'm using pandoc and in my template.tex exists this code to make the paragraphs and subparagraphs to behave like sections.  % Redefines (sub)paragraphs to behave more like sections \ifx\paragraph\undefined\else \let\oldparagraph\paragraph \renewcommand{\paragraph}[1]{\oldparagraph{#1}\mbox{}} \fi \ifx\subparagraph\undefined\else \let\oldsubparagraph\subparagraph \renewcommand{\subparagraph}[1]{\oldsubparagraph{#1}\mbox{}} \fi   This code generate number like this:  1. chapter  1.1 section  1.1.1 subsection  1.1.1.1 subsubsection  1.1.1.1.1 paragraph  1.1.1.1.1.1 subparagraph   How to change this code to enumerate with letter like this:  1. chapter  1.1 section  1.1.1 subsection  1.1.1.1 subsubsection  1.1.1.1.a paragraph  1.1.1.1.a.a subparagraph GeoReference tiff image into the Google map? I want to Geo-reference a tiff image contain a Map for a specific region, I need to add this region(image) and Geo-reference it on the Google map, SO I can see on the map for the region I select the image which I have inserted.  the image also need information such as the Latitude and Longitude of corners and size, and the pixel per meter measurement.  How to do the correct Geo-reference for that ?