Degrees of freedom of massless boson and fermion fields in any even dimension

Abstract

This is a discussion on degrees of freedom of massless fermion and boson fields, if they are free or weakly interacting. We generalize the gauge fields of $S^{ab}$ - $\omega_{abc}$ - and of $\tilde{S}^{ab}$ - $ \tilde{\omega}_{abc}$ - of the spin-charge-family to the gauge fields of all possible products of $\gamma^a$'s and of all possible products of $\tilde{\gamma}^a$'s, the first taking care in the {\it spin-charge-family} theory of the spins and charges quantum numbers ($\tau^{Ai}=\sum_{a,b} c^{Ai}{}_{ab} \,S^{ab}$) of fermions, the second ($\tilde{\tau}^{Ai}= \sum_{a,b} \tilde{c}^{Ai}{}_{ab}\, \tilde{S}^{ab}$) taking care of the families quantum numbers.