ABSTRACT
Nowadays the non-associative structures begin to play an important role in the physics, for instance, non-associative objects such as 3-cocycles are linked with the chiral anomalies in field theory, there is a violation of the Jacobi identity in the quantum mechanics with the Dirac monopole, etc. Keeping in mind more general approaches to field theory, it would be reasonable to consider the generalized theory of fibre bundles based on the non-associative extension of Lie groups. This will allow to construct non-associative gauge theories which involve a higher “non-associative gauge symmetry”. This chapter presents the nonassociative generalization of the theory of principal fibre bundles said to be principal Q-bundles. It also reviews the connection, curvature and Bianchi identities.
