- #1
xuphys
- 7
- 0
Hi,
When I do the following transformation:
$$
X_1=x_1+x_2 \\
X_2=x_2
$$
It turns out that the Jacobian ##\partial (X_1,X_2)/\partial (x_1,x_2)## is 1. But we have:
$$
dx_1dx_1+dx_1dx_2=d(x_1+x_2)dx_2=dX_1dX_2=|\partial (X_1,X_2)/\partial (x_1,x_2)|dx_1dx_2=dx_1dx_2
$$
So we have ##dx_1dx_1=0##. Is this kind of weird? Why does ##(dx_1)^2## have to be 0?
Thank you!
When I do the following transformation:
$$
X_1=x_1+x_2 \\
X_2=x_2
$$
It turns out that the Jacobian ##\partial (X_1,X_2)/\partial (x_1,x_2)## is 1. But we have:
$$
dx_1dx_1+dx_1dx_2=d(x_1+x_2)dx_2=dX_1dX_2=|\partial (X_1,X_2)/\partial (x_1,x_2)|dx_1dx_2=dx_1dx_2
$$
So we have ##dx_1dx_1=0##. Is this kind of weird? Why does ##(dx_1)^2## have to be 0?
Thank you!
Last edited: