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The p-slash operator in spherical coordinates

  1. Jul 7, 2010 #1
    1. The problem statement, all variables and given/known data

    You know the p-slash operator in Cartesian coordinates:
    [tex]{p_{slash}} = {\gamma _\mu }{p^\mu } = {\gamma _0}{p_0} - \vec \gamma \bullet {\bf{\vec p}}[/tex]

    ...but what is p-slash operator in spherical coordinates?

    2. Relevant equations

    - spherical coordinate transformation
    - |x| and t are in reverse-sense, as prescribed by Minkowski metric

    3. The attempt at a solution

    My solution-attempt is at the stage of "brainstorming". Specifically:

    Does only the "r" part get a minus sign, and the "t" part stay positive (I'm thinking the Minkowski metric here), while the "theta" and "phi" part stay as-is?

    But theta and phi, I remember, get mixed up, somehow, in Lorentz boosts...
  2. jcsd
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