On tensor product generators of the gamma matrices.
Posted by peeterjoot on June 20, 2011
In  he writes
The Pauli matrices I had seen, but not the matrices, nor the notation. Strangerep in physicsforums points out that the is a Kronecker matrix product, a special kind of tensor product . Let’s do the exersize of reverse engineering the matrices as suggested.
Let’s start with . We want
By inspection we must have
Thus . How about ? For that matrix we have
Again by inspection we must have
This one is also just the Pauli matrix. For the last we have
Our last tau matrix is thus
Curious that there are two notations used in the same page for exactly the same thing? It appears that I wasn’t the only person confused about this.
The bivector expansion
Zee writes his wedge products with the commutator, adding a complex factor
Let’s try the direct product notation to expand and . That first is
which is what was expected. The second bivector, for is zero, and for is
 A. Zee. Quantum field theory in a nutshell. Universities Press, 2005.
 Wikipedia. Tensor product — wikipedia, the free encyclopedia [online]. 2011. [Online; accessed 21-June-2011]. http://en.wikipedia.org/w/index.php?title=Tensor_product&oldid=418002023.