Timeline for Identifying a scalar function
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 17, 2015 at 9:43 | comment | added | zzz | Regarding the scalar density - if you and I are thinking about the same thing I think the extra factor comes from transformation of the volume element under the same integral | |
| Feb 17, 2015 at 9:32 | comment | added | zzz | Here we have a scalar field - maps to $\mathbb{R}$ don't pick up factors under pullbacks, e.g. see the wiki article linked above. | |
| Feb 17, 2015 at 9:14 | comment | added | Bence Racskó | Contrast this with a so-called scalar density, which is also a scalar-valued field, but picks up the pullback's determinant as a factor, that is something that is scalar valued, but "does not transform as a scalar". | |
| Feb 17, 2015 at 9:13 | comment | added | Bence Racskó | I question this a bit. Of course you are technically correct, but I don't think physicists call scalar fields "scalar" when they are invariant under maps. Rather this means that when you have for example a $\phi(x^1,...,x^n)$ field, then if you have some coordinate change expressible as $x^i=x^i(y^1,...y^n)$ then if you plug this directly into the field, it won't change, whereas a tensor field expressed in components would have their components changed in the usual manner. | |
| Feb 17, 2015 at 8:21 | history | answered | zzz | CC BY-SA 3.0 |