# Lagrangian and scalar field

1. Jan 18, 2014

### shounakbhatta

Can you please tell me whether I am right or wrong?

Lagrangians are scalars. They are NOT invariant under coordinate transformations[ the simplest example is when you have a gravitational potential(V=mgz) and you translate z by "a"(some number). L=1/2*m*(dz/dt)^2-mgz--->L=1/2*m*(dz/dt)^2-mgz-mga, thus the Lagrangian changed under this coordinate transformation!]. However Euler-Lagrange equations ARE invariant under coordinate transformations. So some scalars do vary under coordinate transformation! Thus components of vectors are scalars, thus time is. Again, try to say the following sentence:"the vector <a> is the first component of the vector <b>".

Does not make any sense?

Thanks