Timeline for Is the Higgs mechanism a gauge transformation or not? ( $U(1)$ context )
Current License: CC BY-SA 3.0
16 events
| when toggle format | what | by | license | comment | |
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| Aug 9, 2021 at 4:27 | answer | added | Florence | timeline score: 2 | |
| Feb 15, 2016 at 23:54 | answer | added | Cosmas Zachos | timeline score: 1 | |
| Nov 21, 2015 at 20:52 | vote | accept | karky | ||
| Nov 21, 2015 at 17:59 | answer | added | ACuriousMind♦ | timeline score: 0 | |
| Nov 21, 2015 at 17:13 | comment | added | karky | If we absorb the exponential into $\phi$, so as to get the real field alone, then the $\frac{1}{q}\partial_{\mu}\xi$ term multiplies itself into the kinetic term and leaves us with $\xi$ terms all over the place in the end. | |
| Nov 21, 2015 at 17:01 | comment | added | karky | @ACuriousMind What confuses me is the fact that if you transform like $$ \begin{cases} \phi\rightarrow e^{-i\xi}\phi\\ A_{\mu}\rightarrow A_{\mu}-\frac{1}{q}\partial_{\mu}\left(-\xi\right)=A_{\mu}+\frac{1}{q}\partial_{\mu}\xi \end{cases} $$ then the Lagrangian, as invariant under these transformations, retains its original form for the field $\phi $, but that that is not what we want since then the Lagrangian has an exponential of $\xi$ and the field is not gauged away. | |
| Nov 21, 2015 at 16:59 | comment | added | David Z | @ACuriousMind that sounds like it could be an answer | |
| Nov 21, 2015 at 14:51 | comment | added | ACuriousMind♦ | I don't understand your question. When you have $\theta' = 0$, you have exactly gauged away the $\xi$ phase that was there before, i.e. the gauge transformation $\phi\mapsto \mathrm{e}^{-\mathrm{i}\xi}\phi$ leaves you with $\mathrm{e}^{-\mathrm{i}\xi}\phi = \frac{1}{\sqrt{2}}(\rho + v)$. You don't transform by $\theta'$, you transform with $\theta$, and for $\theta = -\xi$, you get the desired form. | |
| Nov 21, 2015 at 14:39 | history | edited | karky | CC BY-SA 3.0 |
deleted 8 characters in body
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| Nov 21, 2015 at 13:20 | history | edited | Qmechanic♦ | CC BY-SA 3.0 |
square brackets in title are normally reserved to denote moderator actions
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| Nov 21, 2015 at 13:02 | comment | added | karky | Thanks for the suggestions, I reworked the title and the question to be more specific. | |
| Nov 21, 2015 at 13:02 | history | edited | karky | CC BY-SA 3.0 |
Reworked Title and Question
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| Nov 21, 2015 at 11:22 | comment | added | David Z | Hi karky, and welcome to Physics Stack Exchange! This is an okay question as is, but I think a couple things are holding it back from being a great question: first, "Am I looking at this the right way?" is kind of vague. What other way do you think you could be looking at it, or what exactly makes you think the way you're looking at it now might not be valid? Also, "Higgs U(1) mechanism question" is not a very good title. If you address the first thing, it will probably suggest a better title. We have some tips on writing good titles. | |
| Nov 21, 2015 at 0:50 | history | edited | karky | CC BY-SA 3.0 |
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| Nov 21, 2015 at 0:36 | review | First posts | |||
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| Nov 21, 2015 at 0:31 | history | asked | karky | CC BY-SA 3.0 |