Gamma_5 matrix

Question

Hi Kasper,

How can I tell cadabra2 about the \gamma{5} matrix? If I declare it to be ::GammaMatrix, then it mixes with the other \gamma{\mu} when I run joingamma() and sortspinors().

Thanks!

Answer 1

If you're working on four dimensions, $\gamma^5$ is proportional to the product of the four (elemental) gamma's. Therefore you can define something like

{s,r,l,k,m,n,p}::Indices(vector); 
{s,r,l,k,m,n,p}::Integer(0..3); 
\Gamma_{#}::GammaMatrix(metric=\delta); 
e_{\mu\nu\lambda\rho}::EpsilonTensor(delta=\delta);
\delta_{m n}::KroneckerDelta;

g5 := e_{l m n p} \Gamma^{l m n p};

You have to normalise this definition accordingly.

Remember that Cadabra has a definition for the imaginary number

i::ImaginaryI;