- #1

nicouh

- 3

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## Homework Statement

The task is to show the invariance of a given Lagrangian (http://www.fysast.uu.se/~leupold/qft-2011/tasks.pdf" ), but my problem is just in one step (which i got from Peskin & Schröder, page 70) which i can not reproduce due to my lack of knowledge regarding spinors.

The step i am talking about is 3.147 in the attached picture or written out:

## Homework Equations

[itex] C \bar \psi \psi C = (-i \gamma^0 \gamma^2 \psi)^T (-i \bar \psi \gamma^0 \gamma^2)^T [/itex]

[itex] = -\gamma^0_{ab}\gamma^2_{bc} \psi_c \bar \psi_d \gamma^0_{de}

\gamma^2_{ea} [/itex]

[itex] = \bar \psi_d \gamma^0_{de} \gamma^2_{ea} \gamma^0_{ab} \gamma^0_{bc} \psi_c[/itex]

[itex] = -\bar \psi \gamma^2 \gamma^0 \gamma^0 \gamma^2 \psi [/itex]

[itex] = \bar \psi \psi [/itex]

## The Attempt at a Solution

Well, i browsed through Wikipedia, Google and Friends, but did not find anything.

I know how to handle the gamma matrices (like their commutation relations or [itex](\gamma^0)^2 = 1[/itex]) .

I have just no clue what these indices mean, why they are sorted the way they are ("a

__b b__

*c c*

__d d__e" instead of e.g. "ab cd ef gh") and how [itex]\psi^T [/itex] gets converted to [itex]\psi [/itex].

Thanks!

Regards,

Nico

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