1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Covariant, how do you tell?

  1. Jan 5, 2005 #1
    How can you tell if an equation is covariant just by looking at it. Please try and keep explaniation to text more than equations.
     
  2. jcsd
  3. Jan 5, 2005 #2

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    There are basically two criteria:
    1.The equation must contain only quantities with the same type of greek/spacetime indices summed over.Wrt to indices,the equation must be 'balanced',that is the tensor rank of the RHS must be equal to the tensor rank of the LHS.
    2.The sides of the equation must have the same 'tensor quality' (i made it up).You cannot have an equality between a tensor (e.g.in the LHS) and a nontensor (in the LHS).

    Daniel.

    PS.The equation
    [tex] A^{i}=F^{\mu i}B_{\mu} [/tex]
    is not covariant.
     
  4. Jan 5, 2005 #3
    Thank you for your great explaniation. But could you explain the example:

    [tex] A^{i}=F^{\mu i}B_{\mu} [/tex]


    I think I'm having problems due to my lack of understanding with tensors and covariance, no fault of your explaniation.
     
  5. Jan 5, 2005 #4

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    It's basically the "F" 'animal'.The way it's given,it's not a tensor because:
    a) one index takes 4 values and the other only 3.
    b) both indices should behave the same at a general coordinate transformation,but the trouble is that one index transforms with the normal matrix (4*4),while the other with another one,which has only (3*3) components.

    Daniel.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Covariant, how do you tell?
  1. How do you prove this? (Replies: 4)

  2. How do you (Replies: 4)

  3. How do you solve this? (Replies: 11)

  4. How do you do this? (Replies: 2)

Loading...