A Gamma matrix identities

1. Feb 17, 2017

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?

2. Feb 18, 2017

haushofer

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

3. Feb 18, 2017

Staff: Mentor

Aren't they obviously basis independent?

It is the charge conjugation operator.