Timeline for Euler-Lagrange equation for a section of complex line bundle
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Dec 18, 2022 at 7:48 | comment | added | Igor Khavkine | No charts needed to define the directional (or Fréchet) derivatives. There are too many references to pick just one canonical one, but see for example Classical Field Theory by Deligne & Freed from Quantum fields and strings: a course for mathematicians (AMS, 1999). | |
| S Dec 18, 2022 at 7:33 | history | suggested | Buzz | CC BY-SA 4.0 |
typos corrected
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| Dec 18, 2022 at 4:51 | review | Suggested edits | |||
| S Dec 18, 2022 at 7:33 | |||||
| Dec 18, 2022 at 2:55 | history | edited | ChoMedit | CC BY-SA 4.0 |
added 548 characters in body
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| Dec 18, 2022 at 2:47 | comment | added | ChoMedit | @IgorKhavkine I apologize for that.. I now clarify where my confusion is. In fact, why did you say that the chart is unnecessary complicated? Are there something good tools to get a field equations from action functional without trivializations? I mean, most of people doesn't have an attention on specific local expression of the field equation? | |
| Dec 17, 2022 at 22:25 | comment | added | Igor Khavkine | I don't think this is the right place for a "please check my work" request. Even then, you haven't indicated where your own confusion might be in this (unnecessary complicated by charts) calculation. | |
| Dec 17, 2022 at 15:59 | comment | added | ChoMedit | @IgorKhavkine Sorry for lack of rigour. I introduce charts and trivializations to get a Euler-Lagrange equation of given action functional, since the field is not a complex function on $\mathbb{R}^n$, but the section of arbitrary complex line bundle on some manifold $M$. I don't know much about this. But, I've seen this in some paper. Could I ask what is the potential confusion? I didn't intend something physical, but only mathematical. If it were possible, then it would be good, but it makes the problem a little sophisticated and so, I wouldn't check I goes to the right direction. | |
| Dec 17, 2022 at 10:44 | comment | added | Igor Khavkine | I don't understand. Where is the potential confusion? And why introduce charts and trivializations in the first place? | |
| Dec 16, 2022 at 17:03 | history | asked | ChoMedit | CC BY-SA 4.0 |