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In Griffith's Introduction to Elementary Particles, the Dirac equation is given during its derivation as (Equation 7.19):

$$ \gamma ^ \mu p_\mu - mc = 0 $$

However, the dimensions don't seem to make sense, since each element of $\gamma$ (that is, each $\gamma^\mu$) is a 4x4 matrix and each element of $p$ is a number. How does this equation make sense?

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There is an implied 4x4 identity matrix on the $mc$ term.

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