(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find out what p[slash]p[slash] is (Feynman slash-notation), because Maple doesn't like it when you feed it p[slash]p[slash], and let it uber-"FOIL" out the (four non-commuting terms) x (four non-commuting terms), where the "x" denotes plain Jane matrix-multiplication.

2. Relevant equations

[tex]\begin{array}{c}

[{\partial _\mu },{\gamma _\nu }] \equiv 0 \\

{\gamma _0}^2 = - {\gamma _i}^2 \equiv {\bf{I}} \\

\end{array}[/tex]

3. The attempt at a solution

[tex]\begin{array}{c}

{p_{{\rm{slash}}}}{p_{{\rm{slash}}}} = - ({\gamma _\mu }{\partial ^\mu })({\gamma _\nu }{\partial ^\nu }) \\

= - \left( {{\gamma _0}{\partial ^0} - \vec \gamma \bullet \vec \partial } \right)\left( {{\gamma _0}{\partial ^0} - \vec \gamma \bullet \vec \partial } \right) \\

= - \left( {{\gamma _0}^2{{({\partial ^0})}^2} + (\vec \gamma \bullet \vec \gamma ){\nabla ^2} - 2({\gamma _0}{\partial ^0})(\vec \gamma \bullet \vec \partial )} \right) \\

{p_{{\rm{slash}}}}{p_{{\rm{slash}}}} = - \left( {({\bf{I}}){{({\partial ^0})}^2} + ( - 3{\bf{I}}){\nabla ^2} - 2({\gamma _0}{\partial ^0})(\vec \gamma \bullet \vec \partial )} \right) \\

\end{array}[/tex]

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# Homework Help: Trying to Make a (p[slash])^2 operator - is this right?

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