In relativistic physics, paricularly in General Relativity and Quantum Field Theory, we often find the use of the two terms 'invariance' and 'covariance'. But I couldn't find any mention of the difference between the two terms.
Are these two terms different or are they same? What do they exactly mean?
The two terms invariant and covariant have different, though somewhat similar meaning.
Invariant: Any physical quantity is invariant when its value remains unchanged under coordinate or symmetry transformations. Examples are physical quantities represented by scalars, such as temperature, pressure etc. whose value remains the same.
Covariant: The term covariant is usually used when the equations of physical systems are unchanged under coordinate transformations. Physical quantities represented by tensors and appearing in tensorial equations are covariant. Relativistic equations are covariant in the sense that they retain the same form in every coordinate system.
