Note on $Spin(3,1)$ tensors, the Dirac field and $GL(k,\mathbb{R})$ symmetry

H. Arodź, Z. Świerczyński

We show that the rank decomposition of a real matrix $r$, which is a $Spin(3,1)$ tensor, leads to $2k$ Majorana bispinors, where $k=rankr$. The Majorana bispinors are determine…