Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

  1. Jun 19, 2011 #1
    In Zee's Quantum Field theory book he writes

    [tex]\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} [/tex]

    The Pauli matrices [itex]\sigma^i[/itex] I've seen. However, I have two questions

    1) What are these [itex]\tau_i[/itex] matrices?
    2) I'm not familiar with this [itex]\otimes[/itex] notation.
  2. jcsd
  3. Jun 20, 2011 #2


    User Avatar
    Science Advisor

  4. Jun 20, 2011 #3
    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?
  5. Jun 21, 2011 #4


    User Avatar
    Science Advisor

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

    I don't use tau's myself.

    BTW, your earlier expression for gamma^i doesn't match Zee's.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook