- #1
jason12345
- 108
- 0
For an infinitesimal mapping with u = 1,2,3,4:
x ^u \rightarrow x^u + \xi^u(x)
Now suppose we introduce a new set of variables:
x^{'u} = x^{'u}(x)
I would have thought the infinitesimal mapping in terms of the new variables should be written as:
\xi^{'u}(x^{'}) = \frac{\partial \xi^{u}(x)}{\partial x^p} x^{'p} (x)
However, it is written as:
\xi^{'u}(x^{'}) = \frac{\partial x^{'u}}{\partial x^u} \xi^{u} (x)
Does this look correct to you?
x ^u \rightarrow x^u + \xi^u(x)
Now suppose we introduce a new set of variables:
x^{'u} = x^{'u}(x)
I would have thought the infinitesimal mapping in terms of the new variables should be written as:
\xi^{'u}(x^{'}) = \frac{\partial \xi^{u}(x)}{\partial x^p} x^{'p} (x)
However, it is written as:
\xi^{'u}(x^{'}) = \frac{\partial x^{'u}}{\partial x^u} \xi^{u} (x)
Does this look correct to you?
