The axial field and quantum states of fermions in closed configurations

Two real vector fields emerge as spin connections of the fermion field introduced as a representation of the local Lorentz group by Dirac spinors. One of these fields is identified (following V.Fock [1]) as the electromagnetic field. The second axial field is sufficient to describe parity non-conserving effects in atoms and it is sensitive to the second internal degree of freedom [2] of a Dirac spinor field. The quantum number related to this degree of freedom is a distinctive characteristic of a fermion in a spatially closed finite-size state. An intrinsic flexibility of microscopic dynamics in fermion systems that facilitates their transformations is found.