Fermionization, Number of Families

TL;DR

This paper examines the relationship between fermions and bosons through fermionization, aiming to refine the counting rules for degrees of freedom and explore implications for the number of particle families in fundamental physics.

Contribution

It corrects and extends the old fermion-boson counting rule, applying it to the spin-charge-family theory to better understand the predicted number of fermion families.

Findings

Fermionization rules influence the predicted number of fermion families.

Corrections to the old rule may reconcile theory with observed three families.

Unphysical states in higher-dimensional boson systems need further understanding.

Abstract

We investigate bosonization/fermionization for free massless fermions being equivalent to free massless bosons with the purpose of checking and correcting the old rule by Aratyn and one of us (H.B.F.N.) for the number of boson species relative to the number of fermion species which is required to have bosonization possible. An important application of such a counting of degrees of freedom relation would be to invoke restrictions on the number of families that could be possible under the assumption, that all the fermions in nature are the result of fermionizing a system of boson species. Since a theory of fundamental fermions can be accused for not being properly local because of having anticommutativity at space like distances rather than commutation as is more physically reasonable to require, it is in fact called for to have all fermions arising from fermionization of bosons. To make a realistic scenario with the fermions all coming from fermionizing some bosons we should still have at least some not fermionized bosons and we are driven towards that being a gravitational field, that is not fermionized. Essentially we reach the spin-charge-families theory by one of us (N.S.M.B.) with the detail that the number of fermion components and therefore of families get determined from what possibilities for fermionization will finally turn out to exist. The spin-charge-family theory has long been plagued by predicting 4 families rather than the phenomenologically more favoured 3. Unfortunately we do not yet understand well enough the unphysical negative norm square components in the system of bosons that can fermionize in higher dimensions because we have no working high dimensional case of fermionization. But suspecting they involve gauge fields with complicated unphysical state systems the corrections from such states could putatively improve the family number prediction.