Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Basis vectors and abstract index notation

  1. May 1, 2012 #1
    First of all, I'd like to say hi to all the peole here on the forum!

    Now to my question:

    When reading some general relativity articles, I came upon this strange notation:

    T[itex]^{a}[/itex][itex]_{b}[/itex] = C(dt)[itex]^{a}[/itex](∂[itex]_{t}[/itex])[itex]_{b}[/itex] + D(∂[itex]_{t}[/itex])[itex]^{a}[/itex](dt)[itex]_{b}[/itex]. Can someone please explain to me what this means? Clearly the author is trying to use the abstract index notation but I'm used to think of dx[itex]^{i}[/itex] as the covector basis and ∂[itex]_{i}[/itex] as the vector basis thus you're not allowed to change the co- or contravariance of these in an expression.

    Thank you,
    Branislav
     
  2. jcsd
  3. May 1, 2012 #2

    DrGreg

    User Avatar
    Science Advisor
    Gold Member

    Follow the usual rules for raising and lowering indices, e.g.[tex]
    (dt)_a = g_{ab}\,(dt)^b
    [/tex]
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook




Loading...
Similar Threads for Basis vectors abstract Date
I Basis vectors and inner product Apr 14, 2018
B Minkowski metric, scalar product, why the minus sign? Sep 18, 2017
I Constructing a vector in another basis Mar 11, 2017
I Understanding dual basis Mar 13, 2016
Basis vectors of Minkowski space Oct 2, 2015