How Do Gamma Matrix Identities Relate to the Charge Conjugation Operator?

[Bala Tala]

Consider the matrix $C = \gamma^{0}\gamma^{2}$.

It is easy to prove the relations

$$C^{2}=1$$
$$C\gamma^{\mu}C = -(\gamma^{\mu})^{T}$$

in the chiral basis of the gamma matrices.1. Do the two identities hold in any arbitrary basis of the gamma matrices?

2. How is $C$ related to the charge conjugation operator?

 

[haushofer]

Van Proeyen's Tools for Supersymmetry should be helpful :)

 

[PeterDonis]

Do the two identities hold in any arbitrary basis of the gamma matrices?

Aren't they obviously basis independent?

How is $C$ related to the charge conjugation operator?

It is the charge conjugation operator.