SR & Lorentz Scalar Fields: Covariant Diff. & Wave Amplitude

[dyn]

Hi. In GR , covariant differentiation is used because the basis vectors are not constant. But , what about in SR ? If the basis vectors are not Cartesian then they are not constant. Does covariant differentiation exist in SR ? And are for example spherical polar basis vectors which are not constant treated differently to Cartesian basis vectors in SR ?

Another question I have is regarding Lorentz Scalar Fields. I have read that a wave can be treated as a Lorentz scalar field which means that its amplitude in one frame is the same as measured in any other inertial frame but why is the wave amplitude not Lorentz contracted ?
Thanks

 

[andrewkirk]

But , what about in SR ? If the basis vectors are not Cartesian then they are not constant.

Yes, it is needed with non-Cartesian coordinate systems. Some texts use that as a gentle way to introduce the Christoffel symbols. IIRC, Schutz does that in 'A first course in General Relativity', with a chapter introducing Christoffel symbols et al, mostly focusing on polar coordinate systems, before he introduces curvature in the following chapter.

 

[Orodruin]

Just to clarify further, this is nothing particular for Minkowski space - it is the case for any set of non-affine coordinates on a regular euclidean space as well.

 

[dyn]

Thanks. So if I was working with spherical polars in Minkowski space I would use covariant differentiation as the basis vectors are not constant.
Any thoughts on my problem with wave amplitudes and Lorentz scalar fields ?