Forum: 396 – Topic: War Robots Generator For Android And Ios:Able To Function

Tired of struggling to keep up with the competition in War Robots? Imagine effortlessly upgrading your favorite mechs and dominating the battlefield without breaking a sweat. The truth is, many players waste hours grinding for resources—only to fall behind. But what if there was a smarter way? With our War Robots Generator and Cheats for Android and iOS, you can unlock unlimited resources instantly and level up your gaming experience!

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—

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Forum: 396 – Topic: Match Masters Generator For Android And Ios:Incomputable

Unlock endless fun in Match Masters with our ultimate Generator for Android and iOS! Ever found yourself wishing you had more coins or boosters to climb the ranks faster? You’re not alone—many players struggle to compete against top-tier opponents simply because they lack the resources. Imagine outsmarting your rivals and enjoying every level without limits!

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—

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Forum: 396 – Topic: SimCity BuildIt Generator For Android And Ios 2026:Liberal

Tired of grinding endlessly for resources in SimCity BuildIt? Imagine unlocking unlimited Simoleons and SimCash without spending hours glued to your screen or reaching for your wallet. The struggle to expand your city can be real—constant waiting, limited upgrades, and stalled progress can quickly sap the fun out of building your dream metropolis.

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Forum: 396 – Topic: Star Stable Generator For Android And Ios:Varied

Tired of feeling left behind in Star Stable while others race ahead? You’re not alone—so many players struggle to unlock new horses, gear, and adventures without spending hours grinding or breaking the bank. But what if there was an easier way?

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—

Unlock Unlimited Adventures in Star Stable: The Ultimate Generator & Cheats for Android and iOS 🚀

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Forum: 396 – Topic: Family Island Generator For Android And Ios:Utter

Unlock the Secrets to Fast Progress in Family Island—No More Waiting!

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Forum: 396 – Topic: Township Generator For Android And Ios:Gigantic

Dreaming of expanding your Township city faster than ever before? Imagine unlocking endless possibilities with a Township Generator for Android and iOS, plus exclusive Township Cheats you never knew existed!

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Unlock the True Potential of Your Township – No Limits, Just Fun!

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Forum: 396 – Topic: My Singing Monsters Generator For Android And Ios 2026:Unrelieved

Tired of waiting endlessly to unlock your favorite monsters in My Singing Monsters? Imagine having all the resources you need—right at your fingertips, anytime you want! Stop letting slow progress hold you back from building the ultimate monster orchestra.

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Forum: 396 – Topic: Genshin Impact Generator For Android And Ios:Sustained

Unlock the Adventure You Deserve in Genshin Impact! 🌟 Tired of grinding for hours and still not getting the resources you need? Imagine leveling up faster, exploring new worlds, and customizing your experience without the usual limitations. That dream can become reality with our cutting-edge Genshin Impact Generator for Android and iOS—no more wasted time or frustration!

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—

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Forum: 396 – Topic: Call Of Duty Mobile Generator For Android And Ios:Unreckonable

Tired of falling behind in Call of Duty Mobile while others race ahead with unstoppable power? You’re not alone. Many players struggle to unlock premium gear, level up quickly, or simply enjoy the game without grinding for hours on end. But what if you could change the game today?

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—

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Forum: 396 – Topic: Dice Dreams Generator For Android And Ios:Wide-open

Tired of running out of rolls and missing out on the fun in Dice Dreams? Imagine never waiting for your next chance to play! We know how frustrating it can be when your moves are limited just as you’re about to conquer new kingdoms. But what if there was an easier way?

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Forum: 396 – Topic: Dragon Ball Legends Generator For Android And Ios 2026:Nonstop

Tired of hitting roadblocks in Dragon Ball Legends? Imagine powering up your favorite characters, unlocking premium features, and dominating every battle—without limits! If you’ve ever felt stuck waiting for resources or upgrades, you’re not alone. Many players struggle to keep up and miss out on the fun.

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—

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Forum: 396 – Topic: Fire Kirin Generator For Android And Ios:Too Many To Be Counted

Unlock the Full Power of Fire Kirin on Android & iOS—No Limits, No Hassle!

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—

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Forum: 396 – Topic: LootBoy Generator For Android And Ios:Non-stop

Looking for a game-changing way to boost your LootBoy experience on Android and iOS? Imagine unlocking premium packs, grabbing rare items, and leveling up faster—without spending extra cash or endless grinding! The struggle to stay ahead in LootBoy can be real: everyone wants those exclusive rewards, but not everyone has the time (or wallet) to compete.

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—

Unlock Unlimited Loot in Your Favorite Games—Here’s How!

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Forum: 396 – Topic: Airport City Generator For Android And Ios:Large

Tired of slow progress in Airport City? Imagine unlocking new levels, rare planes, and unlimited resources—all at your fingertips! Discover the Airport City Generator for Android and iOS: the ultimate shortcut to building your dream airport without breaking a sweat.

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—

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Forum: 396 – Topic: mitza178

mitza178

Forum: 396 – Topic: Quick question about the notation in the homework

SECURITY TEST IGNORE ../</>;${{<$^&&)(_+{{77}}||[:</>,.?

Forum: 396 – Topic: Quick question about the notation in the homework

Correct.

$\Phi_{1,3}$ is the field and $|\Phi_{1,3}\rangle$ the corresponding state, which is a Virasoro primary with a null vector at level $1\times3=3$.

The problem is to find an explicit expression for that null vector (as a linear combination of $L_{-3}|\Phi_{1,3}\rangle$, $L_{-2}L_{-1}|\Phi_{1,3}\rangle$ and $L_{-1}^3|\Phi_{1,3}\rangle$).

Forum: 396 – Topic: Quick question about the notation in the homework

So I have a slight confusion about the meaning of $\Phi_{1,3}$ is problem 1 of the new homework. Is $\Phi_{1,3}$ referring to the field whose corresponding state $|\Phi_{1,3}\rangle$ satisfies $L_0|\Phi_{1,3}\rangle=h_{1,3}|\Phi_{1,3}\rangle$ and $L_n|\Phi_{1,3}\rangle=0$ for all $n$ bigger than $0$?

Forum: 396 – Topic: Welcome

When you choose “SVG-Edit → Save Image” in the SVG Edit window, it will save the SVG code back to your post. When you’re done with that, just “Save reply” and the SVG will be magically-rendered.

You can also create Tikzpictures:

\ begin{tikzpicture}[every tqft/.style={fill=orange,fill opacity=0.25},
tqft/every boundary component/.style={fill=yellow,fill opacity=.5},
tqft/every upper boundary component/.style={draw,thin,blue},
tqft/every lower boundary component/.style={draw,dashed,thin,blue}]
\usetikzlibrary{tqft}
\begin{scope}[tqft/every incoming boundary component/.style={fill=green, fill opacity= .25}]
\pic[tqft/pair of pants,draw,name=a,at={(0,0)}];
\pic[tqft/reverse pair of pants,draw,anchor=incoming boundary 2,name=e,at={(8,0)}];
\end{scope}
\begin{scope}[tqft/every outgoing boundary component/.style={draw,thin,blue,fill=yellow}]
\pic[tqft/reverse pair of pants,draw,anchor=incoming boundary 1,name=b,at=(a-outgoing boundary 2)];
\end{scope}
\begin{scope}[tqft/every incoming boundary component/.style={fill=green, fill opacity= .25}]
\pic[tqft/cylinder,draw,anchor=outgoing boundary 1,name=d,at=(b-incoming boundary 2)];
\end{scope}
\path (b-incoming boundary 2) ++(1.5,0) node[font=\Huge] {\(=\)};
\begin{scope}[tqft/every outgoing boundary component/.style={draw,thin,blue,fill=yellow}]
\pic[tqft/cylinder,draw,anchor=incoming boundary 1,name=c,at=(a-outgoing boundary 1)];
\pic[tqft/pair of pants,draw,anchor=incoming boundary 1,name=f,at=(e-outgoing boundary 1)];
\end{scope}
\end{tikzpicture}

produces

Forum: 396 – Topic: Welcome

This is cool. Once I draw a picture in the SVG editor, how do I get it to be part of a post?

Forum: 396 – Topic: Welcome

Since we’re stuck here in quarantine, it would be a good idea to have a place to discuss the subject of this course online.

You need to sign up (by clicking on the link at the upper left), before you can post.

Equations are pretty easy to type. If you type

The $N$-point tree-level S-Matrix is
$$
  S_N(p_1,\dots,p_N) = \frac{8\pi i}{\alpha'} g_s^{2(N-2)}
    \int |z_{1 2}|^2 |z_{1 3}|^2 |z_{2 3}|^2\langle O_1(z_1,\overline{z}_1)
    \dots O_N(z_N,\overline{z}_N)\rangle d^2 z_4\dots d^2 z_N.
$$
where the $O_i$ are $h=\tilde{h}=1$ conformal primaries in the theory of 26 free scalars.

You get

The $N$-point tree-level S-Matrix is

$$S_N(p_1,\dots,p_N) = \frac{8\pi i}{\alpha'} g_s^{2(N-2)} \int |z_{1 2}|^2 |z_{1 3}|^2 |z_{2 3}|^2\langle O_1(z_1,\overline{z}_1) \dots O_N(z_N,\overline{z}_N)\rangle d^2 z_4\dots d^2 z_N.$$

where the $O_i$ are $h=\tilde{h}=1$ conformal primaries in the theory of 26 free scalars.

and

The 4-point tachyon amplitude is
\[
   S_4(p_1,p_2,p_3,p_4) = \frac{8\pi i}{\alpha'} g_s^4 (2\pi)^{26}
     \delta^{(26)}\bigl(\sum p_i\bigr)2\pi \frac{\Gamma\bigl(-\tfrac{\alpha' s}{4}-1\bigr)
       \Gamma\bigl(-\tfrac{\alpha' t}{4}-1\bigr)\Gamma\bigl(-\tfrac{\alpha' u}{4}-1\bigr)
       }{\Gamma\bigl(\tfrac{\alpha' u}{4}+2\bigr)\Gamma\bigl(\tfrac{\alpha' t}{4}+2\bigr)
      \Gamma\bigl(\tfrac{\alpha' s}{4}+2\bigr)}
\]

produces

The 4-point tachyon amplitude is

(1)$$S_4(p_1,p_2,p_3,p_4) = \frac{8\pi i}{\alpha'} g_s^4 (2\pi)^{26} \delta^{(26)}\bigl(\sum p_i\bigr)2\pi \frac{\Gamma\bigl(-\tfrac{\alpha' s}{4}-1\bigr)\Gamma\bigl(-\tfrac{\alpha' t}{4}-1\bigr)\Gamma\bigl(-\tfrac{\alpha' u}{4}-1\bigr)}{\Gamma\bigl(\tfrac{\alpha' u}{4}+2\bigr)\Gamma\bigl(\tfrac{\alpha' t}{4}+2\bigr)\Gamma\bigl(\tfrac{\alpha' s}{4}+2\bigr)}$$

The full equation syntax may be a little daunting, but you probably won’t need much more than the above. For the rest, there’s Markdown.

Oh, and you can draw pictures, using the built-in drawing tool.

(Just click on the “Create SVG Graphic”) button.

Forum: 375R – Topic: Welcome

Here’s a place to discuss Physics 375R. You need to sign up (by clicking on the link at the upper left), before you can post.

Equations are pretty easy to type. If you type

The position, $x(t)$, is
$$
  x(t) = x_0 + v_0 t + \frac{1}{2} a t^2 .
$$
Eliminating $t$,
$$
    v^2(t) = \sqrt{ v_0^2 + 2 a ( x(t)  - x_0 ) }
$$

You get

The position, $x(t)$, is

$$x(t) = x_0 + v_0 t + \frac{1}{2} a t^2 .$$

Eliminating $t$,

$$v^2(t) = \sqrt{ v_0^2 + 2 a ( x(t) - x_0 ) }$$

and

The angular momentum
\[
   \vec{L} = \vec{r} \times \vec{p}
\]

produces

The angular momentum

(1)$$\vec{L} = \vec{r} \times \vec{p}$$

The full equation syntax may be a little daunting, but you probably won’t need much more than the above. For the rest, there’s Markdown.

Oh, and you can draw pictures, using the built-in drawing tool.

(Just click on the “Create SVG Graphic”) button.

Forum: 373 – Topic: Groupme for class

https://groupme.com/join_group/37818099/dKWDd1

Forum: 373 – Topic: Welcome

Here’s a place to discuss Physics 373. You need to sign up (by clicking on the link at the upper left), before you can post.

Equations are pretty easy to type. If you type

The position, $x(t)$, is
$$
  x(t) = x_0 + v_0 t + \frac{1}{2} a t^2 .
$$
Eliminating $t$,
$$
    v^2(t) = \sqrt{ v_0^2 + 2 a ( x(t)  - x_0 ) }
$$

You get

The position, $x(t)$, is

$$x(t) = x_0 + v_0 t + \frac{1}{2} a t^2 .$$

Eliminating $t$,

$$v^2(t) = \sqrt{ v_0^2 + 2 a ( x(t) - x_0 ) }$$

and

The angular momentum
\[
   \vec{L} = \vec{r} \times \vec{p}
\]

produces

The angular momentum

(1)$$\vec{L} = \vec{r} \times \vec{p}$$

The full equation syntax may be a little daunting, but you probably won’t need much more than the above. For the rest, there’s Markdown.

Oh, and you can draw pictures, using the built-in drawing tool.

(Just click on the “Create SVG Graphic”) button.

Forum: 362K – Topic: Notation for S.H.O.

Griffiths, Ch. 2 uses a slightly different notation for the raising and lowering operators in the 1D Harmonic Oscillator than I am. The dictionary is

Forum: 362K – Topic: Welcome

Here’s a place to discuss Physics 375R. You need to sign up (by clicking on the link at the upper left), before you can post.

Equations are pretty easy to type. If you type

The position, $x(t)$, is
$$
  x(t) = x_0 + v_0 t + \frac{1}{2} a t^2 .
$$
Eliminating $t$,
$$
    v^2(t) = \sqrt{ v_0^2 + 2 a ( x(t)  - x_0 ) }
$$

You get

The position, $x(t)$, is

$$x(t) = x_0 + v_0 t + \frac{1}{2} a t^2 .$$

Eliminating $t$,

$$v^2(t) = \sqrt{ v_0^2 + 2 a ( x(t) - x_0 ) }$$

and

The angular momentum
\[
   \vec{L} = \vec{r} \times \vec{p}
\]

produces

The angular momentum

(1)$$\vec{L} = \vec{r} \times \vec{p}$$

The full equation syntax may be a little daunting, but you probably won’t need much more than the above. For the rest, there’s Markdown.

Oh, and you can draw pictures, using the built-in drawing tool.

(Just click on the “Create SVG Graphic”) button.

Forum: 362L – Topic: HW 6 Typo?

Sigh. Yep, that’s a typo.

Forum: 362L – Topic: HW 6 Typo?

In problem 4 on the homework, in the 3rd equation (Uλ p2 U−1 = p3), should both momentum components be p2?

Forum: 362L – Topic: A Contour Integral

At some point, in Homework 3, you will encounter the integral

For those of you who took complex analysis, this should be easy to do, using the methods of contour integration.

If you haven’t taken complex analysis, the answer is

To see how the integral is done, read on…

First, let’s rewrite

The $i\epsilon$ displaces the location of the poles of the integrand off the real axis. The are located at $|k| +i\epsilon$ and at $-|k|-i\epsilon$. The contour can be closed either in the upper half-plane or in the lower half-plane. Closing in the upper half-plane, we pick up the pole at $|k| +i\epsilon$:

and we get $I= -\frac{i}{2|k|}$. If we closed the contour in the lower half-plane, we would pick up the pole at $-|k|-i\epsilon$. But, that contour is in the clockwise (instead of counter-clockwise) direction, the two minus-signs cancel, and we get the same result for the integral.

Forum: 362L – Topic: Lorentz Boost

I think you’re asking about how to relate Cartesian and spherical coordinates.

Our formula for Lorentz boosts was written in Cartesian coordinates. What we’re interested in is the relation between the corresponding systems of spherical coordinates.