# Lorentz invariance vs. covariance

I am a bit confused whether relativistic theory is Lorentz invariant or covariant. And please explain why?

As I recall, covariant refers to how an object transforms when you boost to another inertial frame. An example would be the relativistic 4-momentum $P^{\mu}$. Invariant refers to quantities which are unchanged under boosts to different frames. For example the product $P^{\mu}P_{\mu}=m$ has the same numerical value in any frame. Sometimes a relativistic theory is called manifestly covariant if all of the terms in the equations are covariant. The theory is Lorentz invariant if the form of the equations are the same in any inertial frame related by Lorentz transformations.