- #1

- 1,271

- 7

## Homework Statement

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]

## Homework Equations

## 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?