honghao

According to Clifford Algebras, the gamma matrix is very fundermental,
but as we know, electro-weak interaction is chiral, so it seems that
chiral weyl spinor is more fundermental. Who can tell me which is more
fundermental?

thoovler

None of them are any more fundamental than any other. A four
dimensional Clifford algebra contains 16 independent basis elements.
One scalar (1), four vectors (gamma_mu), six bivectors (sigma_mu_nu),
four pseudovectors (gamma5*gamma_mu), and one pseudoscalar (gamma5).
The way these elements are defined as four by four complex matrices
varies with the representation (and there are several of them), but
the breakdown is still the same.