NOTE ON SPIN(3,1) TENSORS, THE DIRAC FIELD AND GL(k,R) SYMMETRY.

We show that the rank decomposition of a real matrix r, which is a Spin(3,1) tensor, leads to 2k Majorana bispinors, where k = rank r. The Majorana bispinors are determined up to local GL(k,R) transformations. The bispinors are combined in pairs to form k complex Dirac fields. We analyze in detail the case k = 1, in which there is just one Dirac field with the well-known standard Lagrangian. The GL(1,R) symmetry gives rise to a new conserved current, different from the well-known U(1) current. The U(1) symmetry is present too. All global continuous internal symmetries in the k = 1 case form the SO(2,1) group. As a side result, we clarify the discussed in literature issue whether there exist algebraic constraints for the matrix r which would be equivalent to the condition rank r = 1. [ABSTRACT FROM AUTHOR]