Totally Anti-symmetric Spinor Tensors in Minkowski Space

Abstract

The spinor tensor ${\epsilon }_{AB}$ has a special property that its elements can be formulated into an algebraic expression of the indices. All the totally anti-symmetric tensors in Minkowski space are expressed by ${\epsilon }_{AB}$. By using the property, we give a simple proof of the total anti-symmetry for the volume spinor tensor.