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- TL;DR Summary
- The Lagrangian for scalar field under translation

The Lagrangian, $$\mathcal L(x)= \frac 1 2 \partial^{\mu} \phi (x) \partial_{\mu} \phi (x) - \frac 1 2 m^2 \phi (x)^2$$ for a scalar field ##\phi (x)## is said to be Lorentz invariant and to transform covariantly under translation.

What does it mean that it transforms covariantly under translation?

What does it mean that it transforms covariantly under translation?