The p-slash operator in spherical coordinates

[bjnartowt]

Homework Statement

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

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

Homework Equations

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

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...

 

[NateD]

so how does that affect the p-slash operator?Also: the gamma matrices have to be decomposed according to spherical coordinates... but I'm not sure how.