Nöther formalism for conserved quantities in classical gauge field theories. II. The arbitrary Bosonic matter case

A formalism suited to deal with Bosonic matter represented by tensor densities coupled with a gauge field and gravitational field is developed. Nöther conserved currents and superpotentials are found and the relation between the canonical and the Hilbert stress tensors are investigated in the general case. The particular cases of gauge theories with scalar matter fields and of purely geometrical theories with arbitrary matter are recovered from this general formalism; as an example of application we consider scalar densities and the vector matter fields.