Spinorielle Feldtheorien und Noether-Theorem in der gekrümmten Raum-Zeit

On the basis of a curved space-time with RIEMANNEAN geometry the conception of spinors is analyzed. It is shown that a consequent treatment of spinors as invariants with respect to coordinate transformations (SOMMERFELD’S first point of view) gives the well known energy-momentum-tensor and the correct spin integral. For this purpose it is necessary to develop NOETHER’S theorem in such a way that not the metric tensor gmn but the metric spintensor is the fundamental metrical quantity. This fact is the cause that the BELINFANTE tensor expression cannot be applied. A new tensor expression for spinor fields is derived. In this connection DIRAC’S theory and HEISENBERG’S theory are investigated.