Going from non-relativistic quantum mechanics(QM) to QFT there is a marked change in the approach used. QM almost exclusively uses Hamiltonains. Lagrangian based methods like the path-integrals are seldom used. In QFT a Lagrangian based approach seems to be more widespread, although  Hamiltonians can also be used. Why is this so? Is the reason historical or is it a matter of " this method works better for this situation"? Or does it have anything to do with the relativistic nature of QFT?
Why does Quantum Field Theory use usually Lagrangians rather than Hamiltonains?  I heard many reasons, but I'm not sure which is true.   Some say it's just a matter of beauty, so Lagrangians are more beautiful because they don't break/separate the space-time variables (so space-time is a single variable, like in the Klein-Gordon Lagrangian and Hamiltonian).  Some say that Hamiltonians are not always Lorentz invariant.  Could someone explain in a little bit more details?
In an extract I am dealing with, I have 2 datetime columns. One column stores the dates and another the times as shown.  How can I query the table to combine these two fields into 1 column of type datetime?  Dates  2009-03-12 00:00:00.000 2009-03-26 00:00:00.000 2009-03-26 00:00:00.000   Times  1899-12-30 12:30:00.000 1899-12-30 10:00:00.000 1899-12-30 10:00:00.000 Obtain the joint PDF of $\theta_{1} - \theta_{2}$ and $\theta_{1}$ where $\theta_{1}$ and $\theta_{2}$ are i.i.d $\text{Uniform}[0, 2\pi)$ I have 2 i.i.d Uniform random variables $\theta_{1}$ and $\theta_{2}$ on $[0, 2\pi)$. Here the problem pushes us to consider that all operations are made modulo $2\pi$. My question is how to obtain the joint PDF of $\theta_{1} - \theta_{2}$ and $\theta_{1}$ and then obtain the conditional PDF of $\theta_{1}$ given $\theta_{1} - \theta_{2}$??. For the second part It can be deduced from the first by writing it as the joint PDF divided by the PDF of $\theta_{1}$. But for the first part, A common idea that I saw is to derive the $\text{CDF}(x, y) = P(\theta_{1} - \theta_{2} \le x$, $\theta_{1} \le y$) and then perform derivations respect to $x$ and $y$. Is this a right approach? If yes, how to proceed with CDF especially with our uniform distribution restrictions? Capitalization for a bullet list Show that $ \sum_{n=2}^m \binom{n}{2} = \binom{m+1}{3}$ What is the advantage to crushed garlic over minced garlic beyond texture? I use a lot of garlic in my cooking, especially minced garlic.  But lately I've been doing some more recipes with crushed garlic and while I love the texture of cooked garlic, I can't see how it could be better than minced garlic for the overall taste.  Is there an advantage to crushed garlic over minced garlic, beyond texture? Finding volume of a segment How to get width of the video and scale another video to that width using ffmpeg? I'm using ffmpeg to stack two videos vertically. They might be different size so I need to scale them to same size. I have found following commands.  First one works for different sizes (but won't scale to proper size):  ffmpeg -i input1 -i input2 -filter_complex '[0:v]pad=iw:ih*2[int];[int][1:v]overlay=0:H/2[vid]' -map [vid] -c:v libx264 -crf 23 -preset veryfast output   Second one works if videos have same width and same pixel format:  ffmpeg -i input1 -i input2 -filter_complex vstack output   How to get width of first input inside complex filter argument so second input could be scaled to same width? What would be the command to do so? I would prefer vstack filter since it should be faster than combination of pad and overlay. Unzip a file with php "Items collection must be empty before using ItemsSource." I'm trying to get images to display in a WPF ListView styled like a WrapPanel as described in this old ATC Avalon Team article: .    When I try to populate the ListView with a LINQ-to-Entities queried collection of ADO.NET Entity Framework objects I get the following exception:  Exception     Items collection must be empty before   using ItemsSource.   My code&hellip;  Visual Basic  Private Sub Window1_Loaded(...) Handles MyBase.Loaded     ListViewImages.ItemsSource = From g In db.Graphic _                                  Order By g.DateAdded Ascending _                                  Select g End Sub   XAML  &lt;ListView Name="ListViewImages"           SelectionMode="Single"           ItemsSource="{Binding}"&gt;     &lt;local:ImageView /&gt; &lt;/ListView&gt;   I put a breakpoint on that line.  ListViewImages.ItemsSource is Nothing just before the LINQ assignment. Nilpotent matrix and basis for $F^n$ "Z-level" in TikZ Drawing a 3D cylinder, and a circle shape on the x---y plane I'm trying to draw a cylinder on the three dimensional space, and I also want its projection on the x--y plane. I found the first answer  to be very useful. I just copy-paste it to my document, and modify it as follows (the modifications are only inside the \begin{tikzpicture} tags):   \documentclass[parskip]{scrartcl} \usepackage[margin=15mm]{geometry} \usepackage{tikz}  \pgfmathsetmacro{\xdeg}{30} \pgfmathsetmacro{\xx}{cos(\xdeg)} \pgfmathsetmacro{\xy}{sin(\xdeg)}  \pgfmathsetmacro{\ydeg}{120} \pgfmathsetmacro{\yx}{cos(\ydeg)} \pgfmathsetmacro{\yy}{sin(\ydeg)}  \pgfmathsetmacro{\zdeg}{80} \pgfmathsetmacro{\zx}{cos(\zdeg)} \pgfmathsetmacro{\zy}{sin(\zdeg)}  \newcommand{\tdcyl}[5]{% origin x, origin y, origin z, radius, height     \path (1,0,0);     \pgfgetlastxy{\cylxx}{\cylxy}     \path (0,1,0);     \pgfgetlastxy{\cylyx}{\cylyy}     \path (0,0,1);     \pgfgetlastxy{\cylzx}{\cylzy}     \pgfmathsetmacro{\cylt}{(\cylzy * \cylyx - \cylzx * \cylyy)/ (\cylzy * \cylxx - \cylzx * \cylxy)}     \pgfmathsetmacro{\ang}{atan(\cylt)}     \pgfmathsetmacro{\ct}{1/sqrt(1 + (\cylt)^2)}     \pgfmathsetmacro{\st}{\cylt * \ct}     \filldraw[fill=white] (#4*\ct+#1,#4*\st+#2,#3) -- ++(0,0,#5) arc[start angle=\ang,delta angle=-180,radius=#4] -- ++(0,0,-#5) arc[start angle=\ang+180,delta angle=180,radius=#4];     \filldraw[fill=white] (#1,#2,#3+#5) circle[radius=#4]; }       \begin{tikzpicture}[x={(\xx*1cm,\xy*1cm)},y={(\yx*1cm,\yy*1cm)},z={(\zx*1cm,\zy*1cm)}]          \tdcyl{-3}{-3}{0}{1}{3} % x y z   r h         \tdcyl{0}{0}{0}{1}{3} % x y z   r h           \draw (-3,0,0) -- (3,0,0) node[circle,fill=white] {x};         \draw (0,-3,0) -- (0,3,0) node[circle] {y};         \draw (0,0,-3) -- (0,0,3) node[circle] {z};     \end{tikzpicture}     \end{document}   I added another cylinder and tweaked the positions to fit what I need. This produces the following:      Which is almost what I want, except that I want to see the projection of that cylinder on the x--y plane, but unfortunately, the top cylinder hides the full circle. When I disable the top cylinder:      \begin{tikzpicture}[x={(\xx*1cm,\xy*1cm)},y={(\yx*1cm,\yy*1cm)},z={(\zx*1cm,\zy*1cm)}]          \tdcyl{-3}{-3}{0}{1}{3} % x y z   r h            \draw (-3,0,0) -- (3,0,0) node[circle,fill=white] {x};         \draw (0,-3,0) -- (0,3,0) node[circle] {y};         \draw (0,0,-3) -- (0,0,3) node[circle] {z};     \end{tikzpicture}   Now the projection is shown again:   But the top cylinder is missing...  How can I make the top cylinder transparent, or, alternatively, and even better; how do I create one long cylinder and emphasize its projection on the x--y plane?   BTW, what determines the position of the labels x,y,z in the above code? I want to reposition them so they won't overlap with the axis. Thanks in advanced! What are the prerequisites to encounter the legendaries in ORAS? There are a lot of legendaries available in ORAS, however a lot of them will only show up/be available if certain prerequisites are met.  I know Groudon/Kyogre are available through the Story, and      Rayquaza &amp; Deoxys   through the postgame Delta episode, but what about the other available legendaries? What do I need to do to catch them? How to determine whether a given Linux is 32 bit or 64 bit? When I type uname -a, it gives the following output.  Linux mars 2.6.9-67.0.15.ELsmp #1 SMP Tue Apr 22 13:50:33 EDT 2008 i686 i686 i386 GNU/Linux   How can I know from this that the given OS is 32 or 64 bit?  This is useful when writing configure scripts, for example: what architecture am I building for? Batch file to create Folder based on Date and Copy Files from One Location to Another Location? I want to supply constant voltage to my LED's but the supply varies from 3.7V to 4.2V (Li-ion battery). I cannot use 3.3V voltage regulator as it will need at least 4.3V voltage at the input but my battery can supply only 4.2V max. so is there any other way I can supply regulated 3.3V to my LED.   RGB LED = 3.3V, 60mA Battery = 3.7V - 4.2V, 3000mA Number of LEDs = 24 The LED's are connected in parallel "sudo -u postgres psql postgres" does not ask for password With OpenDNS now needing one to be on the pro package to have filtering turned on, being on a tight budget, we are in need of free DNS filtering.  After reading , I collected SquidGuard blacklists and concatenated domains in the categories i needed into one big list. I then fed it to  generating a file containing about 2 million zones.  named-checkconf parses it just fine, but reloading named takes almost 10 minutes, then it wont resolve anything, and the server slows down to a crawl. Removing the include results in named working properly again.  Whats the proper way to set up BIND9 to work as a DNS firewall efficiently? If it's possible to also block any domain that resolves to specific IP addresses that would solve the whole problem.   I'm running bind as non-authoritative, just a caching server. sort but keep header line at the top I am getting output from a program that first produces one line that is a bunch of column headers, and then a bunch of lines of data. I want to cut various columns of this output and view it sorted according to various columns. Without the headers, the cutting and sorting is easily accomplished via the -k option to sort along with cut or awk to view a subset of the columns. However, this method of sorting mixes the column headers in with the rest of the lines of output. Is there an easy way to keep the headers at the top? Restricted logins with automatic full permission in databases My scenario: I have some groups with full - and inappropriate - access to all Sql Server instances. I want to change that.  My Plan: Give full and automatic access to all databases (it is customer databases and this groups must be allowed to change any property if necessary).  Restrict permissions on Instance Level, because this groups should not be allowed to do any unexpected change on instance properties.  I don't want to create a user in databases, because our external customer could drop the user ( they have db_owner permission )  Someone have any idea? Tks