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How do i figure this out?

Anonymous Tue 19 Apr 09:30:32 2022 No.14408866 View Reply Original Report

Quoted By: >>14408874

Under a local gauge transformation, what will be the constraint on eta? I tried transforming the antisymmetric vector boson field, and the field it self, but that seems to complicate things. Help me bros ive spent an embarassing amount of time on this.

Anonymous

Anonymous Tue 19 Apr 2022 09:39:19 No.14408874 Report

Quoted By: >>14408896 >>14408899

>>14408866
>I tried transforming the antisymmetric vector boson field, and the field it self
Well that would have been my suggestion.

Anonymous

Anonymous Tue 19 Apr 2022 10:04:14 No.14408896 Report

Quoted By: >>14408899

>>14408874 This is what i have.
$-ig(\rho^\dagger_{\alpha\beta}+\eta\rho_{\alpha\beta}\rho^{\dagger\alpha}+(1-\eta)i\rho^{\dagger}_{\alpha}\rho^\alpha\partial^{\beta}\theta + i\partial^{\alpha}\theta(\eta\rho_{\beta}\rho^{\dagger\alpha}-\rho^{\dagger}_{\beta}\rho^{\alpha}))({A^\beta + \partial^\beta \theta})$

Anonymous

Anonymous Tue 19 Apr 2022 10:07:52 No.14408899 Report

Quoted By: >>14408915

>>14408896
shit should be this instead:

>>14408874 This is what i have.
$-ig(\rho^\dagger_{\alpha\beta}\rho^\alpha +\eta\rho_{\alpha\beta}\rho^{\dagger\alpha}+(1-\eta)i\rho^{\dagger}_{\alpha}\rho^\alpha\partial^{\beta}\theta + i\partial^{\alpha}\theta(\eta\rho_{\beta}\rho^{\dagger\alpha}-\rho^{\dagger}_{\beta}\rho^{\alpha}))({A^\beta + \partial^\beta \theta})$

Anonymous

Anonymous Tue 19 Apr 2022 10:23:59 No.14408915 Report

Quoted By: >>14408922

>>14408899
QFT was quite a while ago for me so I'll probably not be able to help, but after you've transformed your fields do you need to impose some condition for the Lagrangian to remain gauge invariant?

Anonymous

Anonymous Tue 19 Apr 2022 10:30:03 No.14408922 Report

Quoted By: >>14408933

>>14408915
$\delta\textit{L}=0$ i guess?

Anonymous

Anonymous Tue 19 Apr 2022 10:43:06 No.14408933 Report

Quoted By: >>14408935

>>14408922
Sorry I might be confusing matters here, it's the one procedure I remember doing a lot. But that was typically do deduce an interaction term.
https://en.m.wikipedia.org/wiki/Gauge_principle
The cited book (Lagrangian Interaction) is where I originally learned about it, I can recommend it. I was wondering if you could use the same idea to find a constraint on eta, but I don't know.

Anonymous

Anonymous Tue 19 Apr 2022 10:45:19 No.14408935 Report

Quoted By:

>>14408933
ok thanks dude.

Anonymous

Anonymous Tue 19 Apr 2022 11:46:55 No.14409008 Report

Quoted By: >>14409035

This looks like gauge fixing. Are you trying to derive the Fadeev Popov ghost fields?

Anonymous

Anonymous Tue 19 Apr 2022 12:04:31 No.14409035 Report

Quoted By:

>>14409008
no, nothing to do with ghosts or g fixing. it was a question on one of my tests; we just needed to use hermiticity and gauge invariance of the lagrangian to determine constraints on the constants.

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