Timeline for Twisted Chern-Simons, and Twisted Wess-Zumino Term
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Aug 3, 2018 at 9:09 | comment | added | Xenomorph | @ Sunghyuk Park Do you have any references for twisted cohomology that are easy for physics students? | |
| Aug 3, 2018 at 3:47 | comment | added | Henry | @NewStudent Thanks for clarification. I guess the "generalized second Chern class" is closed only under $D_a$ but not $d$, so probably make sense as an element of the twisted cohomology. | |
| Aug 2, 2018 at 19:35 | comment | added | Xenomorph | Do you think it makes sense to talk about the "generalized" second Chern-class $\mathrm{Tr}((D_{a}B+B\wedge B)\wedge(D_{a}B+B\wedge B))$? | |
| Aug 2, 2018 at 19:32 | history | edited | Xenomorph | CC BY-SA 4.0 |
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| Aug 2, 2018 at 19:31 | comment | added | Xenomorph | $U^{-1}D_{a}U=U^{-1}dU+U^{-1}aU$. This is Lie algebra-valued. | |
| Aug 2, 2018 at 18:08 | comment | added | Henry | So it seems that your question should be whether the infinitesimal generalized Wess-Zumino term vanishes? | |
| Aug 2, 2018 at 18:06 | comment | added | Henry | What's the meaning of $U^{-1}D_a U$ exactly? Assume that $G$ is simply connected and fix a trivialization of the bundle $P$. $U$ is a map from $M$ to $G$ ($G$-valued function on $M$). $U^{-1}dU$ is originally defined to be the pullback of the Maurer-Cartan 1-form on $G$ via $U$. But now you want to apply covariant derivative $D_a$ on $U$. $U$ is not $\mathfrak{g}$-valued but $G$-valued. So you might want to apply infinitesimal gauge transformation, rather than an actual gauge transformation. Then you're gauge transformation will be $\mathfrak{g}$-valued. | |
| Jul 31, 2018 at 22:28 | history | edited | Xenomorph | CC BY-SA 4.0 |
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| Jul 31, 2018 at 16:56 | comment | added | Qmechanic | Crossposted to physics.stackexchange.com/q/420415/2451 | |
| Jul 31, 2018 at 16:34 | history | asked | Xenomorph | CC BY-SA 4.0 |