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

TL;DR

This paper discusses the degrees of freedom of massless boson and fermion fields in even dimensions, exploring their gauge fields and quantum numbers within the spin-charge-family framework.

Contribution

It generalizes gauge fields associated with spin and family quantum numbers to all possible products of gamma matrices in even dimensions.

Findings

Degrees of freedom depend on spacetime dimension.

Generalization of gauge fields to all gamma matrix products.

Implications for spin-charge-family theory.

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.