- #1

- 149

- 4

## Homework Statement

Prove that [itex]\gamma^{a}\gamma^{b}\gamma^{c}\gamma^{d}\gamma^{e}\gamma_{a}[/itex] = [itex]2\left(\gamma^{e}\gamma^{b}\gamma^{c}\gamma^{d}+\gamma^{d}\gamma^{c} \gamma^{b}\gamma^{e}\right)[/itex]

Each of the [itex]\gamma^{i}[/itex]s are as used in the Dirac equation.

## Homework Equations

[itex]\gamma^{a}\gamma^{b}\gamma^{c}\gamma^{d}\gamma_{a}[/itex] = [itex]-2\gamma^{d}\gamma^{c}\gamma^{b}[/itex]

[itex]\gamma^{a}\gamma^{b} + \gamma^{b}\gamma^{a} = 2g^{ab}[/itex]

## The Attempt at a Solution

[itex]\gamma^{a}\gamma^{b}\gamma^{c}\gamma^{d}\gamma^{e}\gamma_{a}[/itex] = [itex]2g^{ab}\gamma^{c}\gamma^{d}\gamma^{e}\gamma_{a}[/itex] - [itex]\gamma^{b}\gamma^{a}\gamma^{c}\gamma^{d}\gamma^{e}\gamma_{a}[/itex]

= [itex]2\gamma^{c}\gamma^{d}\gamma^{e}\gamma^{b}[/itex] + [itex]2\gamma^{b}\gamma^{e}\gamma^{d}\gamma^{c}[/itex]

Perhaps I mixed up something or there is a typo...