Mathematics

Based on an interpretation of the quark-lepton symmetry in terms of the unimodularity of the color group and on the existence of 3 generations, we develop an argumentation suggesting that the finite quantum space corresponding to the exceptional formally real Jordan algebra of dimension 27 is relevant for the description of internal space in the theory of particles. More generally it is suggested that the replacement of the algebra of real functions on spacetime by the algebra of functions on spacetime with values in a finite-dimensional Euclidean Jordan algebra is relevant in particle physics. This leads us to study the theory of Jordan module and to develop the differential calculus over Jordan algebras. We formulate the corresponding theory of connections.