Timeline for Relating the Yang-Mills field-strength to the Maxwell tensor in $SU(2)$ gauge theory
Current License: CC BY-SA 4.0
19 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| S May 27, 2019 at 17:03 | history | bounty ended | CommunityBot | ||
| S May 27, 2019 at 17:03 | history | notice removed | CommunityBot | ||
| May 27, 2019 at 0:08 | vote | accept | Othin | ||
| May 24, 2019 at 18:07 | vote | accept | Othin | ||
| May 27, 2019 at 0:08 | |||||
| May 22, 2019 at 0:36 | comment | added | Othin | Well, the solution is not assumed to be BPS here, it's the general case. | |
| May 21, 2019 at 21:30 | vote | accept | Othin | ||
| May 21, 2019 at 21:30 | |||||
| May 19, 2019 at 23:51 | answer | added | Subhaneil Lahiri | timeline score: 3 | |
| May 19, 2019 at 16:32 | comment | added | Subhaneil Lahiri | I don't know that book, but is this in the case of a BPS monopole? Do you also have the Bogomol'nyi equation, $\vec{D}\Phi = \vec{B}$? | |
| S May 19, 2019 at 16:03 | history | bounty started | Othin | ||
| S May 19, 2019 at 16:03 | history | notice added | Othin | Draw attention | |
| S May 18, 2019 at 22:02 | history | bounty ended | CommunityBot | ||
| S May 18, 2019 at 22:02 | history | notice removed | CommunityBot | ||
| May 14, 2019 at 14:43 | comment | added | Othin | Well, about the second part... it's true, but $D_{\mu}\hat{\Phi}=0 $ is a weaker condition. The results must be valid even inside the core, so that the interpretation of the magnetic field as $b_i=-\frac{1}{2}\epsilon_{ijk}f_{jk}$ still holds (in the sense that it remains a valid interpretation).Also, outside of the core we could just use the stronger condition $D_{\mu}\Phi=0$, which must be satisfied far from the origin. | |
| May 12, 2019 at 13:51 | comment | added | David Bar Moshe | Sorry for not posting a full answer, please observe that $\hat{\Phi} B \hat{\Phi} = \mathrm{Tr}( \hat{\Phi} B ) \hat{\Phi}$ for any adjoint quantity $B=\sum_{a=1}^3 B^a t_a$, (such as the gauge potential). As for your second question, please see the remark in Manton and Sutcliffe following equation (8.70), where they explain that this solution is asymptotically valid in the region outside the core of the monopole, where the gauge field Abelianizes. | |
| May 12, 2019 at 9:00 | history | tweeted | twitter.com/StackPhysics/status/1127498825415966720 | ||
| S May 10, 2019 at 20:09 | history | bounty started | Othin | ||
| S May 10, 2019 at 20:09 | history | notice added | Othin | Draw attention | |
| May 8, 2019 at 19:40 | history | edited | Qmechanic♦ | CC BY-SA 4.0 |
edited body; edited title
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| May 8, 2019 at 18:56 | history | asked | Othin | CC BY-SA 4.0 |