# Correct way for symmetry transform

1. Dec 13, 2013

### tamiry

1. The problem statement, all variables and given/known data

Hi
I'm trying to understand how symmetry transform works.
Suppose a lagrangian $L = q^{-2}$
(actually it had another kinetic member, but I dont need it for my question here)

The matching action $S = \int dt q^{-2}$

We were told that it has the next symmetry
$t \rightarrow at$
$q \rightarrow a^{-1/2}q$
I tried to figure how, but I cant get it.

3. The attempt at a solution

I thought the correct way is this
$T = at$
$Q(T) = a^{-1/2}q(T)$

and now I put it in the action
$S = \int dt q^{-2} = \int (dT/a) (q(T))^{-2} = \int (dT/a) (a^{+1/2}*Q(T))^{-2} = \int (dT/a) (a^{-1})*(Q(T))^{-2} = a^{-2}*S ≠ S$

Is that the correct way to do it? Obviously I could change the power of a in t/q transform and it would fix it, is that it?