Speaker
Description
We propose a description of colour triplets of quarks by entangled $Z_3$-graded Lee-Wick type fields, one with real mass and the two remaining ones with mutually conjugate complex masses. This is obtained by attributing colour degrees of freedom to six Pauli spinors, three endowed with colours and three with anti-colours, which are united into one $12$-component generalized "coloured Dirac spinor".
The so entangled triplet of quark fields satisfies a generalized Dirac equation, with generalized $\gamma$-matrices acting on $12$-component coloured spinors. The characteristic sixth order equation satisfied by each component, results from the diagonalization of the system. The sixth-order dispersion relations lead to solutions suitably vanishing
in asymptotic region, exhibiting the well established confinement property of coloured quarks 'degrees of freedom.
We show how one can construct certain cubic combinations of those solutions in a way that cancels the damping factors, producing freely propagating functions.