# Lagrangia is it invariant

1. Jan 19, 2014

### shounakbhatta

Hello,

Is Lagrangian invariant?

I am in a conversation, where one is saying that:

"Shifting the coordinate system changes the value of the potential energy with respect to the same reference level, that's why the Lagrangian changes"

While the other:

"Shifting the coordinate system, doesnt shift the zero reference level of potential for the system..
The reference level of potential is fixed for the system once it is decided upon."

So, is Lagrangian variant or invariant?

Thanks.

2. Jan 20, 2014

### maajdl

The Lagrangian has the symmetries of the system that it represents.

3. Jan 20, 2014

### shounakbhatta

In the case can we consider that is it variant or invariant?

Also, is it a scalar or a vector product?

4. Jan 20, 2014

### BruceW

it depends what the Lagrangian is. some Lagrangian equations will be variant and some will be invariant.

edit: the definition of invariant, is that if you make some change, then the Lagrangian will still look the same. So if you shift the coordinate system but the Lagrangian still looks the same, this means the Lagrangian is invariant with respect to a coordinate shift.

5. Jan 20, 2014

### shounakbhatta

If it is a variant in a equation then it cannot be scalar?

Is it that it becomes scalar as well as a vector?