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4 vectors

  1. May 9, 2007 #1
    1. The problem statement, all variables and given/known data

    Let us define 4 vector by 4 co-ordinates:(x1,x2,x3,x4) where (x1,x2,x3) are space components (like x,y,z) and x4 is related to time as x4=ict.Express the following equations in tensor notation.

    (i)The continuity equation: div J+(del*rho/del t)=0

    (ii)The wave equation del2ψ-(1/c2) [del2 ψ/del t2]=0

    (iii)What will be the value of j4 instead of above?

    2. Relevant equations

    3. The attempt at a solution

    I got totally stuck.Please help me to start with it.
     
  2. jcsd
  3. May 9, 2007 #2

    nrqed

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    Just rewrite all th epartial derivatives with respect to x,y,z and t in terms of partial derivatives with respect to x1, x2, x3, x4.

    Of course, for the first three, it's trivial, i.e.

    [itex] \frac{\partial}{\partial x} = \frac{\partial}{\partial x_1} [/itex] etc. For the time part, you will have a factor of ic appearing in the relation. Now, just replace all your partial derivatives in your equations.
     
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