Timeline for Principal Bundle Connection Correspondence for two descriptions of the $\mathbb{CP}^2$
Current License: CC BY-SA 2.5
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 27, 2010 at 5:34 | vote | accept | Aston Smythe | ||
| Jan 27, 2010 at 4:29 | comment | added | David Bar Moshe | It is possible. You can induce a connection on an associated bundle, thus if you define an action of U(1) on U(2), then you get an associated U(2) bundle on CP2 and you can compute the induced connection. In our case, the action of U(1) on U(2) is trivial because they commute, thus the induction will be trivial. However, if you want to get any U(2) bundle over CP2 (such that the total space is not necessarily SU(3)), then you may define another action of U(1) on U(2) then induce. | |
| Jan 26, 2010 at 23:39 | comment | added | Aston Smythe | I am I right in assuming then that any $U(1)$-connection induces a $U(2)$ connection via the embedding $\mathfrak{u(1)} \to\mathfrak{u(2)}$? | |
| Jan 26, 2010 at 4:26 | history | answered | David Bar Moshe | CC BY-SA 2.5 |