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:

$p\!\!\!/=\gamma ^{\mu }p_{\mu }\,$

$=\gamma ^{0}p_{0}-\gamma ^{i}p_{i}\,$

—Preceding unsigned comment added by 169.234.141.96 (talk • contribs)

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)