Otimes notation and tau matrices used in definition of gamma matrices?

[Peeter]

In Zee's Quantum Field theory book he writes

$$\begin{align}\gamma^0 &= \begin{bmatrix}I & 0 \\ 0 & -I\end{bmatrix}=I \otimes \tau_3 \\ \gamma^i &= \begin{bmatrix}0 & \sigma^i \\ \sigma^i & 0\end{bmatrix}=\sigma^i \otimes \tau_2 \\ \gamma^5 &=\begin{bmatrix}0 & I \\ I & 0\end{bmatrix}=I \otimes \tau_1 \end{align}$$

The Pauli matrices $\sigma^i$ I've seen. However, I have two questions

1) What are these $\tau_i$ matrices?
2) I'm not familiar with this $\otimes$ notation.

 

[strangerep]

2) I'm not familiar with this $\otimes$ notation.

Try Wiki:

http://en.wikipedia.org/wiki/Tensor_product#Kronecker_product_of_two_matrices

That should also allow you to reverse-engineer the tau matrices... :-)

 

[Peeter]

Try Wiki:

http://en.wikipedia.org/wiki/Tensor_product#Kronecker_product_of_two_matrices

That should also allow you to reverse-engineer the tau matrices... :-)

I find that the tau matrices are just the sigma matrices. Odd that two different notations would be used. One notation when defining the gamma matrices in terms sigmas directly, and an entirely different notation when using the tensor product?

 

[strangerep]

I find that the tau matrices are just the sigma matrices.

... which is what Zee says beneath his eq(4) on p90.

Odd that two different notations would be used. One notation when defining the gamma matrices in terms sigmas directly, and an entirely different notation when using the tensor product?

I don't use tau's myself.

BTW, your earlier expression for gamma^i doesn't match Zee's.