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

Is the following a matrix?

Given: these identities (ordinarily in "Feynman slash notation": not sure how to do slashes in LaTeX):

[tex]\begin{array}{c}

({\gamma _\mu }{a^\mu }){\gamma _\nu }{b^\nu } + {\gamma _\nu }{b^\nu }({\gamma _\mu }{a^\mu }) \equiv 2{a_\mu }{b^\mu } \\

({\gamma _\mu }{a^\mu })({\gamma _\mu }{a^\mu }) \equiv {a_\mu }{a^\mu } \\

\end{array}[/tex]

2. Relevant equations

[tex]({\gamma ^\mu }{\partial _\mu })({\gamma ^\nu }{A_\nu }) + ({\gamma ^\nu }{A_\nu })({\gamma ^\mu }{\partial _\mu }) = [/tex] ... a matrix or a vector?

3. The attempt at a solution

Maybe it is a matrix. My final answer needs a matrix answer (specifically: I need the field-strength tensor, [tex] F^{\mu, \nu} [/tex], to pop up eventually.

Maybe it isn't a matrix. The operator [tex] \partial _\mu [/tex] is a differential operator, and A is the four-vector-potential. that suggests I should wind up with a differentiated version of the field-strenght tensor, which would be awfully-boring in a certain gauge I forget the name of (it'd be zero/divergenceless, a la Griffiths Intro Elementary Particles, p. 239-240).

???

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# Homework Help: Is the following a matrix? (yes/no)

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