Talk:Feynman slash notation

Metric convention
For a g=(1,-1,-1,-1) metric, shouldn't the expression


 * $$p\!\!\!/ = \gamma^\mu p_\mu \,$$
 * $$= \gamma^0 p_0 + \gamma^i p_i \,$$
 * }

actually be:



—Preceding unsigned comment added by 169.234.141.96 (talk • contribs)
 * $$p\!\!\!/ = \gamma^\mu p_\mu \,$$
 * $$= \gamma^0 p_0 - \gamma^i p_i \,$$
 * }
 * No, because both $$ \gamma^\mu \,$$ & $$ p_\mu \,$$ are independent of the metric convention. Or put it another way, because the metric does not explicitly appear in the slash definition.


 * Contrast with the definitions:
 * $$\{ \gamma^\mu, \gamma^\nu \} = \pm 2 \eta^{\mu \nu} \,$$
 * and
 * $$ p^2 = \pm p\!\!\!/ p\!\!\!/ \,$$
 * where the $$\pm \,$$ sign is metric convention dependent, + for g(+---) and - for g(-+++).


 * I guess the article should say this.


 * --Michael C. Price talk 11:00, 22 March 2009 (UTC)


 * I agree with the response above, but when lowering indexes you have to take the metric in account. Therefore, is wrong to say that $$\gamma^i p_i = \mathbf{\sigma \cdot p}$$, because the dot product between $$\mathbf{\sigma}$$ and $$\mathbf{p}$$ is the standard inner product of the orthonormal Euclidean space.


 * In this way, I've corrected the signs in the $$p\!\!\!/$$ matrix. You can check on Griffiths, for instance, that the correct form is this one.


 * --André Manoel talk 15:30, 16 September 2009 (UTC)