Foundations of Gyro-gauge theories

A novel mathematical model of color perception based on a quantum mechanical formalism has been developed in prior work by E. Provenzi, M. Berthier et al. Further development of the model, and in particular the modeling of the phenomenon of chromatic induction, requires the investigation of geometric objects analogous to connections on vector bundles and principal bundles – in physics commonly referred to as gauge theories – in which the fibers are replaced by nonassociative algebraic structures known as gyrovector spaces and gyrogroups. We refer to this generalization as "gyro-gauge theories". The aim of this thesis work is to present some preliminary results in this direction specializing to the case of the Einstein gyrogroup, which is relevant to the color model discussed above.