The picture follows the convention of the time axis being on the vertical direction.   I think this Feynman diagram represents Coulomb repulsion between two electrons with a virtual photon being absorbed and emitted by each electron.   What are the arrows on the electron lines for? I'm not sure what information this tells us.
The momentum-space fermion propagator in the free Dirac theory is given by       The arrow on the fermion propagator is said to represent the flow of charge.  How can we derive this statement quantitatively from the Dirac Lagrangian?  What is the quantitative form of the charge being referred to here?
I want to center a div vertically with CSS. I don't want tables or JavaScript, but only pure CSS. I found some solutions, but all of them are missing Internet Explorer 6 support. &lt;body&gt;     &lt;div&gt;Div to be aligned vertically&lt;/div&gt; &lt;/body&gt;  How can I center a div vertically in all major browsers, including Internet Explorer 6? How should I use a possessive apostrophe when a name is between commas? How to force Mac window to foreground? I want to completely replace Ubuntu with Lubuntu Turn off automatic preview in apple mail Is it possible to turn off automatic preview of attachments when composing an e-mail?  NOTE: Yes I know that I can manually ctr+select the attachment and disable preview, but I want this done automatically How do levers amplify forces? This is really bothering me for a long time, because the math is easy to do, but it's still unintuitive for me.  I understand the "law of the lever" and I can do the math and use the torques, or conservation of energy. or whatever... And I can see that a lever can amplify a force you apply to it  if you apply a force on the longer side of the beam.  If I were to look at the molecular lever and see what actually happens when I push on the lever, and I give acceleration to the molecules, how does it actually happen that more force is transmitted to the other side?  Thank you all  p.s I'm looking just for an explanation in terms of forces and acceleration, it's clear to me how to do this in terms of energy or torques Your content must have a ListView whose id attribute is 'android.R.id.list' I've never really thought about how the shell actually executes piped commands. I've always been told that the "stdout of one program gets piped into the stdin of another," as a way of thinking about pipes. So naturally, I thought that in the case of say, A | B, A would run first, then B gets the stdout of A, and uses the stdout of A as its input.    But I've noticed that when people search for a particular process in ps, they'd include grep -v "grep" at the end of the command to make sure that grep doesn't appear in the final output. This means that in the command ps aux | grep "bash" | grep -v "grep" it is implied that ps knew that grep was running and therefore is in the output of ps. But if ps finishes running before its output gets piped to grep, how did it know that grep was running?   flamingtoast@FTOAST-UBUNTU: ~$ ps | grep ".*" PID TTY          TIME CMD 3773 pts/0    00:00:00 bash 3784 pts/0    00:00:00 ps 3785 pts/0    00:00:00 grep I'm trying to recall the title of a young adult-targeted book. It was probably published by Scholastic, or at least sold through their take-home pamphlets, which means it was probably published before I started high school in 1996. It's about a group of teenagers who receive invitations to play a game at an invitation-only arcade. When they go there, they are put in an immersive VR game in which they must learn to survive on an alien planet. I believe the game ends and they wake up back in the real world after they fall asleep on the alien one. They are invited back the the game a couple times, and then it turns out…      …they go to play the game again, but they are unable to exit it. Eventually they realize that they actually are on an alien planet now, and that the previous game-playing sessions were just training for the real thing. I believe the epilogue states that all of the players have coupled up and the females have become pregnant, and they are optimistic about populating the new planet.   I think it was told in the first-person perspective of a female player. I don't think there was a real protagonist or strong conflict; just the group of players learning how to survive in the game. One of the other players had a photographic memory and used it to map the planet's surface. I think the cover art featured of a girl wearing a VR headset over her eyes, with her hair being blown back and her mouth open in surprise. What would you call someone who makes no lasting impression? Evaluation of the limit $\lim\limits_{n \to \infty } \frac1{\sqrt n}\left(1 + \frac1{\sqrt 2 }+\frac1{\sqrt 3 }+\cdots+\frac1{\sqrt n } \right)$ Evaluate the limit : $$\lim_{n \to \infty } {1 \over {\sqrt n }}\left( {1 + {1 \over {\sqrt 2 }} + {1 \over {\sqrt 3 }} + \cdots + {1 \over {\sqrt n }}} \right)$$  I can use the sandwich principle, certain convergence criteria, Cesaro mean theorem, limit arithmetic.. things around this area.  Any help would be greatly appreciated, thanks!  Sorry for not elaborating more at the beginning, rookie first-post mistake I suppose. :) Solve $[2^{(2^{403})}] = [a]$ in $\mathbb Z_{23}$ where $0 \le a < 23$. Solve $[2^{(2^{403})}] = [a]$ in $\mathbb Z_{23}$ where $0 \le a &lt; 23$.  I've tried to combine corollaries of Fermat's little theorem and various other methods to solve this, but have always been stuck. Guaranteed lifetime of temporary in C++? How can I manage computers using my Firefox Sync account? I`m using Firefox Sync on a bunch of computers.   I would like to manage my account, by removing some computers. I can't find the place to do this, it should be on the Firefox Sync page, but the official page only has the privacy and download information. Returning anonymous functions from lapply - what is going wrong? Auto-implemented getters and setters vs. public fields I see a lot of example code for C# classes that does this:  public class Point {     public int x { get; set; }     public int y { get; set; } }   Or, in older code, the same with an explicit private backing value and without the new auto-implemented properties:  public class Point {     private int _x;     private int _y;      public int x {         get { return _x; }         set { _x = value; }     }      public int y {         get { return _y; }         set { _y = value; }     } }   My question is why. Is there any functional difference between doing the above and just making these members public fields, like below?  public class Point {     public int x;     public int y; }   To be clear, I understand the value of getters and setters when you need to do some translation of the underlying data. But in cases where you're just passing the values through, it seems needlessly verbose. Prove that the equation: $c_0+c_1x+\ldots+c_nx^n=0$ has a real solution between 0 and 1. Let $c_0,c_1,c_2,\ldots ,c_n$ be constants such that :  $$c_0+\frac{c_1}{2}+\ldots+\frac{c_{n-1}}{n}+\frac{c_n}{n+1}=0$$  I have to prove that the equation: $$c_0+c_1x+\ldots+c_nx^n=0$$  Has a real solution between 0 and 1.  Didn't know how to start...I thought that maybe I could use something about derivative...But I'm lost... Any help,much appreciated!!! divisibility question in abstract algebra over a field $d|n \Rightarrow x^{p^d} - x$ divides $x^{p^n} - x$ over $\mathbb{F}_{p}$ where $\mathbb{F}$ is a field.  Attempt:   $d|n \Rightarrow x^{p^d} - x$ divides $x^{p^n} - x \Rightarrow x^{p^d - 1} - 1$ divides $x^{p^n - 1} - 1 \Rightarrow p^d - 1$ divides $p^n - 1$ since $p^n - 1 = (p^d)^{\frac{n}{d}}-1$.  How does this look? When using a new Windows 8 search bar:    What is the syntax of the search expression? Is it possible to use wildcards like "*", "?" or any other special symbol?  For example, when searching with Google i can use:   '-' (minus) for excluding certain words; "quoted phrase" for exact phrase matching. Nearby objects won't move independently? I created a thick glass bottle and duplicated the interior faces to make a new object to create the liquid inside.   I went in the edit mode, selected the faces I wanted to copy and duplicated them with ShiftD. Then I pressed P to  separate the duplicated faces.   Now I try to make a duplicate of that liquid to make it flow out of the bottle, and I simply need the duplicate of one face of it. So I go to edit mode and do as I did to make the liquid from the bottle faces... but as soon as I'm back to the object mode and I want to move the duplicated faces, every thing moves with it...   I played around and tried things, and while doing so I realized that if I dupe the liquid object in object mode using ShiftD and press 0 to place it where the original is, they move together if I duplicate it and place it somewhere else so that they are separated.   Also if I pick one of the two separated objects and make it intersect with the other one, release my left mouse button to place it there, and then try to move it again, they both move together, but not at the same speed.  I really don't understand what is going on and I'm sure it's really badly explained, so what I'll do is make a screen capture of my Outliner and record the behavior of the objects and upload those to help you understand.