/sci/ - Science & Math

[OrganicEuphoria !C5Eg6mdVac No.4946430]

Alright /sci/, enough of this highschool babby bullshit, lets get us some real discussion goin'.

Consider the Lagrangian:

<div class="math">\mathbf{L}=-\frac{1}{4}F^{\mu v}F_{\mu v}-\frac{1}{2}m^{2}A_{\mu }A^{\mu }-i\bar{\psi }(\gamma ^{\mu }\partial _{\mu }-m)\psi -eA_{\mu }\bar{\psi }\gamma ^{\mu }\psi</div>

What's the momentum space propagator <span class="math">D_{\mu v} (k)[/spoiler] for the massive fucking vector field <span class="math">A_{\mu }[/spoiler]?

[Anonymous No.4946447]

Do your own homework.

[OrganicEuphoria !C5Eg6mdVac No.4946461]

>>4946447
>implying I can't already do this...


I'm just trying to initiate some ACTUAL mathematics / physics discussion and collaboration.

[Anonymous No.4946465]

What's the stress energy tensor? Standard QED?

[Anonymous No.4946472]

I haven't been doing QFT for quite some time now, so please correct me if I'm wrong. I assume that you know a little bit, and I'm too lazy to TeX it down.

First you write your Lagrangian in a way that your fields A appear as bilinears and drop the terms that don't - so screw the last term, which is only a vertex for A. The terms between the fields A is then a differential operator in real space.

Then you simply do a Fourier transform and replace the derivatives by plus or minus (i k), depending in which direction the derivatives act!

The propagator is then the inverse of that differential operator in momentum space.

A good example is shown in Greiner: Field Quantization, section 7.6 page 188 - available on Google Books.

[Anonymous No.4946478]

>>4946461
90% of /sci/ doesn't know what a Lagrangian is.

grad school circle jerk =/= "actual" math or physics discussion

[Anonymous No.4946481]

>massive
>A

[Anonymous No.4946483]

>>4946481
Well, there clearly is an explicit mass term, bright as fucking day, isn't there?

[Anonymous No.4946484]

>grad school
this is 2nd year undergrad physics. but yes, a very limited amount of people here know field theory

[OrganicEuphoria !C5Eg6mdVac No.4946486]

>>4946472
You sir, are on the right track.
I'm quite sure I know the answer to this, it is relatively easy rQFT. I was primarily curious as to how much of /sci/ is familiar with, and can solve such a problem. I know for sure there's some smart people out there.

[OrganicEuphoria !C5Eg6mdVac No.4946493]

>>4946478
So should we dumb-down discussion to compensate, effectively making /sci/ a more prominent shit-hole then it already is?

[Anonymous No.4946494]

>>4946483
yes, but the Lagrangian is wrong.

[Anonymous No.4946497]

Surely you must be joking, Mr. Organic.

I only read popular science, what is this math of which you speak

[OrganicEuphoria !C5Eg6mdVac No.4946504]

>>4946494
I assure you, it is not.

[Anonymous No.4946505]

>>4946478
>grad school circle jerk =/= "actual" math or physics discussion

that's actually literally what math or physics discussion is

fuck off

[Anonymous No.4946509]

>>4946494
No, why should it be wrong? Sure, it's not gauge invariant anymore and the A's arent gauge fields (like photons), but QED wasn't even mentioned here.

[Anonymous No.4946523]

>dat feel when complex fermion mass

Anyway,
>>4946472
that sceme will work out fine.

>>4946486
not much

>>4946481
It wouldn't be uninteresting to see someone rant about the Yang Mills mass problem (e.g. the need for the higgs mechanism) so go on. I'm actually not sure by heart if the problem applies for the commutative gauge group (as OP is impling U(1)).


But I mean you know that the propagator will just turn out to be the green function, so you can go streight ahead and apply your formal inverse differential operator magic for DG=1
See e.g.
http://en.wikipedia.org/wiki/Pseudo_differential_operator

That is (D+m^2)G=1 <=> G=int exp(-ipx)*/(p^2+m^2)

where D is the d'alambert.

There must be a \mu\nu somewhere, so I figure you plug in another \eta

[Anonymous No.4946524]

>>4946509
> it's not gauge invariant
that's why. i don't believe in working with gauge variant fields. this is post-higgs after all.

[OrganicEuphoria !C5Eg6mdVac No.4946533]

>>4946523
<div class="math">D_{v\sigma }(k)=\frac{-i}{k^{2}-m^{2}+i\epsilon }[\eta _{v\sigma }-\frac{k_{v}k_{\sigma }}{m^{2}}]</div>

Glad to see you're still around man.

[Anonymous No.4946535]

>>4946523
addon:
might well be that the operator is more difficult than just the Klein Gordon one, but not *really* more difficult.
In anyway, I remember the general computation and there the massless propagator being much more a pain in the ass.

[Anonymous No.4946536]

>>4946524
Not every quantum field theory requires gauge fields. I would even say that most phenomenological models don't use gauge invariance - think of e.g. Walecka model.

[Anonymous No.4946540]

>>4946524
You're the definition of a faggot. Go ahead and make a relatively straight forward problem into an autism rage fest with a yang mills non-commutative gauge group

[Anonymous No.4946543]

>>4946536
they arnt fundamental

[Anonymous No.4946547]

>>4946540
calm down. do you prefer people argue over if evolution is true rather than if fields should be gauge invariant?

[Anonymous No.4946548]

>>4946543
And what makes you think this field here is fundamental? Why do I bother? I should go to bed.

[OrganicEuphoria !C5Eg6mdVac No.4946545]

So, how about...

Show that in the large momentum limit, <span class="math">D_{\mu v}(k)[/spoiler] scales as O(1). Show that in terms of momentum counting, <span class="math">A_{\mu }[/spoiler] has an effective dimension 2.

[Anonymous No.4946555]

>>4946548
>>4946547
It's a fucking practice problem. I can define massive vector fields all day blindfolded.

Do they necessarily exist?

Are you some kind of assblasted experimentalist or just a troll?

[OrganicEuphoria !C5Eg6mdVac No.4946559]

Fuck /sci/, this place has gotten even worse.
What the hell happened.

[Anonymous No.4946566]

>>4946559
Eh, it was never that good. Once in a while an interesting thread like this comes along, but not long until it is bombarded by pedantery or trolling.

A good night to you sirs, I'm off to sleep.

[Anonymous No.4946575]

*higgs rant*
yeah, so appearently one can "easily fix" the theory.
http://en.wikipedia.org/wiki/Stueckelberg_action

>>4946545
Don't know what "scales as Z_2" means...
Anway, I'd blingly guess in the large momentum limit the boson becomes the photon with two helicity states?

Going to bed now.

[Anonymous No.4946591]

>>4946575
It looks like some renormalization exercise. I haven't touched Weinberg for a while, but I think you're supposed to rescale the wave vector

[Anonymous No.4946597]

>>4946566
Pedantry.*

Sorry, it was too good to pass up.

[OrganicEuphoria !C5Eg6mdVac No.4946598]

>>4946591
>rescale the wave vector

Yes sir.

[Anonymous No.4946604]

>>4946597
>infantile cartoon

[Anonymous No.4946607]

Something about redoing the photon interaction thingy and keeping track of the mass term with the positive k-powers?

anyway, gn.
come back with an actual discussion, not questions where you have the answer :P

[Anonymous No.4946617]

>>4946604
looks like she has some nice titties

[Anonymous No.4946620]

>>4946617
>fapping to cartoons

How pathetic are you?

[OrganicEuphoria !C5Eg6mdVac No.4946622]

>>4946607
I've tried that man, a sustained discussion just never takes off. But if I run across something of interest I suppose I'll post it up here.

[Anonymous No.4946624]

>>4946620
>calling people pathetic on 4chan
you poor soul

[Anonymous No.4946631]

>>4946624
U mirin' my alphaness, nerd?

[Anonymous No.4946633]

>>4946604
>being an underage high school student shitting up a science thread

[Anonymous No.4946636]

>>4946631

[OrganicEuphoria !C5Eg6mdVac No.4946647]

You're all pathetic, enough shit-posting.

Gonna delete this now.