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Hi, what is the difference between Lorentz Invariance and Lorentz Covariance?

From my lecture note (Group theory course) Invariance and Covariance where defined as follows:

Invariance: refers to the property of objects being left unchanged by symmetry operations.

Covariance: refers to equations whose form is preserved by a change of coordinate system.

From this I had the understanding that Lorentz Invariance refers to physical quantities that do not change under a Lorentz transformation and Lorentz covariance refers to equations that do not change after a coordinates transformations (of course the equation will be going from primed to unprimed after a Lorentz transformation but the structure of equations wouldn’t )

However, I have also read in physics books where the author talks about the invariance of “equations” just one example here “Lorentz Invariance of the Dirac equation”.

Is this because the above definitions are not as solid in physics as in mathematics, or is my understanding of what they meant is wrong, or is it because the authors are being sloppy?

From my lecture note (Group theory course) Invariance and Covariance where defined as follows:

Invariance: refers to the property of objects being left unchanged by symmetry operations.

Covariance: refers to equations whose form is preserved by a change of coordinate system.

From this I had the understanding that Lorentz Invariance refers to physical quantities that do not change under a Lorentz transformation and Lorentz covariance refers to equations that do not change after a coordinates transformations (of course the equation will be going from primed to unprimed after a Lorentz transformation but the structure of equations wouldn’t )

However, I have also read in physics books where the author talks about the invariance of “equations” just one example here “Lorentz Invariance of the Dirac equation”.

Is this because the above definitions are not as solid in physics as in mathematics, or is my understanding of what they meant is wrong, or is it because the authors are being sloppy?

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