1. The problem statement, all variables and given/known data I am trying to prove that [tex]\displaystyle{\not} a \displaystyle{\not} b + \displaystyle{\not} b \displaystyle{\not} a = 2a\cdot b[/tex] using the relation [tex]\{\gamma^{\mu},\gamma^{\nu}\} = 2g^{\mu\nu}[/tex] 2. Relevant equations 3. The attempt at a solution If I work backwards, [tex] 2a\cdot b = 2a_{\mu} g^{\mu \nu} b_{\nu} = a_{\mu}(\gamma^{\mu}\gamma^{\nu})b_{\nu} + a_{\mu}(\gamma^{\nu}\gamma^{\mu})b_{\nu}[/tex] The first term is [tex]\displaystyle{\not} a \displaystyle{\not} b[/tex] but the second term doesn't seem to look like [tex]\displaystyle{\not} b \displaystyle{\not} a[/tex]. Am I missing something here?
You're missing the fact that [itex]a_\mu[/itex] and [itex]b_\nu[/itex] are ordinary numbers, and so commute with everything.