Click HERE to see this thread with all of the graphics, features, and links.

Because I need help simplifying this expression,

http://i.imgur.com/eFIqzq8.png

into this,

http://i.imgur.com/MFIQyRa.png

where the asterisk denotes that it's an irreducible single particle representation, and.

http://i.imgur.com/HL3D1uy.png

You need to carry the 1 into the tens place.

Can't tell if Dadudemon is being helpful or flippant... mhmm

g_serious

No

Originally posted by Omega Vision
Can't tell if Dadudemon is being helpful or flippant... mhmm
It's an algebraic expression, he's making an ass out of himself.

Did you try to reverse the polarity, though?

Have you tried wolfram alpha?

But IDK why you think KMC forums has many people who can do this...

Originally posted by Master Han
Have you tried wolfram alpha?

But IDK why you think KMC forums has many people who can do this...

I don't think receiving help was in any way, shape or form the intention of this thread.

If you can't do calculus you should be in a different line of work.

Originally posted by Astner
Because I need help simplifying this expression,

http://i.imgur.com/eFIqzq8.png

into this,

http://i.imgur.com/MFIQyRa.png

where the asterisk denotes that it's an irreducible single particle representation, and.

http://i.imgur.com/HL3D1uy.png This equation is screwed up, I'm afraid. It deduces that pi exactly 3.

http://i.ytimg.com/vi/O-Y-ua3WBi4/0.jpg

Never-mind, I was able to solve it.

Originally posted by Bardock42
Did you try to reverse the polarity, though?
The expression represents the sum of all connected graphs, with two external photon lines, and with polarization indices μ and ν carrying four-momentum q into and out of a diagram.

Originally posted by Master Han
Have you tried wolfram alpha?
I have Mathematica, and no, it can't be used to solve these type of problems.

Originally posted by Symmetric Chaos
If you can't do calculus you should be in a different line of work.
This isn't calculus, this is group field theory.

Originally posted by Astner
Never-mind, I was able to solve it.

I don't doubt you, but out of curiosity, would you mind posting how you did it?

Originally posted by Master Han
I don't doubt you, but out of curiosity, would you mind posting how you did it?
Yeah, I'm rewriting it in TeX right now. You might have to wait until tomorrow though because it's five pages on paper, and I have work in the morning.

does it make you feel superior to post calculus problems on a forum in which the most popular topics tend to be "which fictional character wins in h2h combat"?

Originally posted by focus4chumps
does it make you feel superior to post calculus problems on a forum in which the most popular topics tend to be "which fictional character wins in h2h combat"?

That's ridiculous.




It makes him feel superior to post group field theory problems on a forum in which the most popular topics tend to be "which fictional character wins in h2h combat"

oh right. what i meant to do was nod my head and pretend to understand like everyone else does in these threads. right ddm?

Originally posted by Astner
Yeah, I'm rewriting it in TeX right now. You might have to wait until tomorrow though because it's five pages on paper, and I have work in the morning.

Um, if you're just doing it for us, it's really ok, lol. But I assume you're not.

Originally posted by Astner
Because I need help simplifying this expression,

http://i.imgur.com/eFIqzq8.png

into this,

http://i.imgur.com/MFIQyRa.png

where the asterisk denotes that it's an irreducible single particle representation, and.

http://i.imgur.com/HL3D1uy.png

This is the calculational equivalent of benching 400 pounds.

Actually, I do find the concept of vacuum polarization fascinating. For me, it really drives home the idea of an active vacuum and of the close relationship between spacetime, matter and energy (or so I think).

Originally posted by Astner
This isn't calculus, this is group field theory.

"This isn't addition, this is adding together the number of eggs in each hen house."

Originally posted by Master Han
Um, if you're just doing it for us, it's really ok, lol. But I assume you're not.

He's worried about his e-penis. This is the equivalent of flashing other dudes in a locker room.

Haha, someone wants to show off.

Originally posted by Astner
Because I need help simplifying this expression,

http://i.imgur.com/eFIqzq8.png

into this,

http://i.imgur.com/MFIQyRa.png

where the asterisk denotes that it's an irreducible single particle representation, and.

http://i.imgur.com/HL3D1uy.png

To answer your question, no, I cannot simplify it. I am not familiar with it enough to simplify it.

The furthest I got was reviewing eigenstates (four-momentum) and spin. We then applied a Lorrentz transformations and the like. We used the standard transformation...because it was an academic setting and that is how they teach things in the beginning (and they add tougher transformations later on).


So, after using that standard transformation against a simple eigenstate four-momentum (defined as "|p, σ >" (but the p has an arrow on top pointing to the right to indicate that momentum/boosted value)...

Standard Lorrentz transformation:
http://i191.photobucket.com/albums/z238/dadudemon/lorrentztransformationofthefourmomentumoperator.png

Result:
http://i191.photobucket.com/albums/z238/dadudemon/lorrentztooureigenstate.png

Please note that I did not use the zero-momentum state for my starting point.


And that is as far as we got. What you're doing is a year or two away from the furthest we got. Also, we probably would have never gotten that far because my major was not quantum physics.


Edit - 313

First off, let's make the multiplication notations clear.

http://i.imgur.com/PnID0Z5.png

The trace of product of gamma matrices of even numbers is given by,

http://i.imgur.com/5S7b7CP.png

For instance,

http://i.imgur.com/sFOur4c.png

http://i.imgur.com/q13fHM4.png

and

http://i.imgur.com/S6hJHzB.png

And for odd numbers of gamma matrices we have,

http://i.imgur.com/4xL1hQh.png

The proof of the initial expressing is through mathematical induction.

http://i.imgur.com/uTa0aYW.png

which is in accordance with the initial expression for the product two gamma matrices. So if this is true for N ≤ M - 1. We now have

http://i.imgur.com/6njUAUA.png

Every commutator have zero trace, so the last term subtracted here is the same as the left-hand side, and so

http://i.imgur.com/x2Swjqg.png

Assume that the initial equation gives the trace of any product of 2N - 2 Dirac matrices, then the last equation shows that the initial equation gives the trace of 2N Dirac matrices.

The easiest way to see that an odd number of Dirac matrices vanishes is to note that -γ_μ is related to γ_μ by a similarity transformation, -γ_μ = γ_5γ_μ (γ_5)^-1. Hence unaffected by those similarity transformations, so the trace of an odd amount of Dirac matrices is equal to minus itself, hence zero.

QED.

Now let's go back to the problem.

The first minus sign in the expression implies the presence of a fermion loop, and is rewritten as

http://i.imgur.com/vbyRpgg.png

Now, let's use the following trick on the equation above

http://i.imgur.com/OwKdUbf.png

and rewrite part of it as

http://i.imgur.com/Nf6AI1R.png

Let p approach p + qx and the equation becomes

http://i.imgur.com/aRWQGss.png

Using the proof above we can easily calculate the trace as,

http://i.imgur.com/gK2JmwX.png

We now Wick rotate and get

http://i.imgur.com/cZG8cLk.png

where

http://i.imgur.com/6KrgmWx.png

Now let

http://i.imgur.com/1qpgtWy.png

http://i.imgur.com/oMrTx4W.png

and replace with Ω, and get

http://i.imgur.com/dGghw3t.png

Also we have that

http://i.imgur.com/kPkiuSF.png

and

http://i.imgur.com/wATtVC4.png

We can now rewrite the expression as,

http://i.imgur.com/l7mdc5G.png

The two terms in the integrand are combined with,

http://i.imgur.com/0eY3s1H.png

and voila, we have the desired expression!

And no, I'm not going to address Mr. Wikipedia making a fool of himself.

Originally posted by Astner
And no, I'm not going to address Mr. Wikipedia making a fool of himself.

Sorry, you can't get what I took images of from Wikipedia.

Originally posted by dadudemon
Sorry, you can't get what I took images of from Wikipedia.
True, you googled them, hence the photobucket links. I doubt you even have LaTeX. You read up on four momentum on Wikipedia though.

And I'll suggest you step down before I drop an expression for you to Lorentz transform.

Originally posted by Astner
True, you googled them, hence the photobucket links. I doubt you even have LaTeX. You read up on four momentum on Wikipedia though.

And I'll suggest you step down before I drop an expression for you to Lorentz transform. Lol did you open this thread just to show off?

Yes?

Astner is a sociopath.

Originally posted by Lord Lucien
Lol did you open this thread just to show off?
No, I was sincerely asking for help.

This shit took me four hours two write, cut, and post. If I wanted to show off I would've gone with something simpler.

Originally posted by Tzeentch._
Yes?

Astner is a sociopath.
Go back to painting your Sisters of Battle miniatures, men are talking.

I believe Astner when he says he was asking for help. Showing off happens to be a side benefit.

Originally posted by Astner
True, you googled them, hence the photobucket links. I doubt you even have LaTeX. You read up on four momentum on Wikipedia though.

And I'll suggest you step down before I drop an expression for you to Lorentz transform.

Honestly...I don't care what you think.


But go ahead and drop the bass.

You're just furious that there is someone else on the internet that knows something about what you assumed was a "niche" and "elite" knowledge set. Only the best and brightest, right? lol

Yeah, this is ridiculous. If I were a global still, I'd close it. There's nowhere else you'd try to go first, before posting a math equation on a ****ing movie dicussion forum?!

Maybe you're being sincere. But, just as an fyi, almost no one's going to buy it.

How come we can discuss psychology, philosophy, politics, biology, and religion, but not physics?

You gotta love Google and ctrl+C/ctrl-V.

Astner, you were educated stupid. You need to start thinking with cubes.

Aww, it's crying. That's adorable.

Originally posted by Astner
How come we can discuss psychology, philosophy, politics, biology, and religion, but not physics?

I'd hate to bandwagon-bash you, but most of the subjects you mention can be discussed by anyone with (or without) some decent critical thinking and research skills. Complex, graduate school level math, and the higher level hard sciences, on the other hand...

Originally posted by Master Han
I'd hate to bandwagon-bash you, but most of the subjects you mention can be discussed by anyone with (or without) some decent critical thinking and research skills. Complex, graduate school level math, and the higher level hard sciences, on the other hand...

Actually one can talk about physics without graduate level math. And we have.

He's just having a kind of hissy fit that's very common along physicists. Once he gets his bottle Astner will be fine.

Yeah how many people here did you think could perform these equations at all, nevermind on par enough with you to offer any insight or "help"? There's bound to be whole forums out there populated with physics majors, so why did you pick the one that you knew would have so very few? Either you totally missed that you were posting on KMC, somehow... or you're trying to show off to everyone how great you are at the science.

Originally posted by Astner
How come we can discuss psychology, philosophy, politics, biology, and religion, but not physics?

You're not really asking this, are you?

Discussing physics on a movie discussion forum can be productive, but what you posted was, at best, irrelevant to anything anyone would care about, and most won't be able to talk about due to the specialized nature of it. Do I really - really - need to explain that?

On the off chance that you weren't just trying to swing your d*ck around amongst a bunch of strangers, I'd almost feel bad for being such a jag-off to you. Just almost, though, because your utter lack of social awareness in posting this is perhaps the greater flaw, especially given your experience with this site.

To everyone else, just be above it. If he's deliberately trolling or looking for a reaction, he already got one, so mission accomplished there. But it doesn't have to go any further than that. I'm not exactly taking my own advice - granted - but no one's perfect.

Originally posted by Astner
True, you googled them, hence the photobucket links.

True physicists use imgur.

Agreed that this thread has no practical purpose and can only cause aggravation- closed.