- #1
Catria
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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...