.Decomposing a 4x4 Matrix into Dirac 16 Matrices

[Neitrino]

Dear All,

Could you pls remind me how do I decompose arbitrary 4x4 matrix into Dirac 16 matrices...

I ve forgotten.

Thank you

 

[Dick]

If your unknown matrix is really a sum of gamma matrices you could try using the defining characteristic of the gamma matrices, {gamma_m,gamma_n}=2*g_mn. But not every 4x4 matrix is a sum of gamma matrices.

 

[George Jones]

But not every 4x4 matrix is a sum of gamma matrices.

I don't know how to answer Neitrino's question, but I think Neitrino is asking about using the gamma matrices and their products to form a basis for the 16-dimensional vector space of 4x4 matrices. Usually, this space is written as a direct sum of subspaces of dimensions 1, 4, 6, 4, 1.