The topic of this paper is the duality matter / fields, studied from the way they are used in models in Physics. A systematic review of the concept of motion leads to a deep understanding of spinors, and to the introduction of a new formalism, based on Clifford algebras, which is easily transposed in the context of General Relativity. Using theorems of Quantum Mechanics proven in a previous paper, it is then possible to give a general definition of matter fields and bosons, including gravitation, and to describe their behaviour, the currents and the energy-momentum tensor, in a Yang-Mills and fiber bundles model in curved space-time.