Are any of you familiar with vacuum polarization beyond the standard model?

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

into this,

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

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:

Result:

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.

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

For instance,

and

And for odd numbers of gamma matrices we have,

The proof of the initial expressing is through mathematical induction.

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

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

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

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

and rewrite part of it as

Let p approach p + qx and the equation becomes

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

We now Wick rotate and get

where

Now let

and replace with Ω, and get

Also we have that

and

We can now rewrite the expression as,

The two terms in the integrand are combined with,

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. 🙂

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.

Yes?

Astner is a sociopath.

Originally posted by Lord Lucien
Lol did you open this thread just to show off?

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.

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

Originally posted by dadudemon
Honestly...I don't care what you think. 🙂

But back to the topic, why would you—who didn't even study physics—be taught how to Lorentz transform four-momentums. On top of that being to Lorentz transform four-momentums by following a methodology you didn't understand?

Originally posted by dadudemon
But go ahead and drop the bass.

Originally posted by dadudemon
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.