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Basis vectors in SR and Lorentz scalar fields

  1. Oct 2, 2015 #1

    dyn

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    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
     
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  3. Oct 2, 2015 #2

    andrewkirk

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    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.
     
  4. Oct 2, 2015 #3

    Orodruin

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    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.
     
  5. Oct 3, 2015 #4

    dyn

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    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 ?
     
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