Differences between Lorentz scalars and Lorentz invariants

[Llewlyn]

Are there any differences between a Lorentz scalar quantity or a Lorentz invariant quantity?
That sound be stupid but we dindt find anything exaustive about that.
Take as example the power irradiate by an accelerated charge (Larmor formula, relativistic one). The expression for evaluating in two frames (rest and lab) are different but they refer to same value (if 10W is in one frame, 10 W is in the other).

Is it a scalar or an invariant?

We really appreciate your help,

Ll.

 

[Mentz114]

As I understand it, scalars are a subset of invariants. So a scalar is an invariant that is not a vector or tensor. No doubt someone will correct this if it's wrong.

 

[HallsofIvy]

The word "invariant" is used in many different ways. The appropriate definition here is "does not change value if we change to a new coordinate system". Of course that is also the definition of "scalar". There is no difference between "invariant" and "scalar" here.

I'm trying to figure out how two formulas could be "different" if the always give the same value!

 

[Llewlyn]

As I understand it, scalars are a subset of invariants. So a scalar is an invariant that is not a vector or tensor. No doubt someone will correct this if it's wrong.

I think you point out correctly.
I find it too this is the most logical way.

Ll.