# Parameters and notation

1. Apr 19, 2006

### flybyme

Hello,

While reading up some about the Pauli matrices (which the author indexes by $\sigma_{00}, \sigma_{01}, \sigma_{10}, \sigma_{11}$) I stumbled across an expression for the multiplication rules:

$\sigma_{ab} \sigma_{a'b'} = i^{\tilde {w} ( a, b ; a', b' ) } \sigma_{a \oplus a', b \oplus b'}$

where $\tilde {w} (a, b ; a', b') \in \mathbb{Z}_4$.

Later an explicit formula for $\tilde {w}$ is given, and it is equal to $ab + a'b' - (a \oplus a')(b \oplus b') + 2a' b \text{ mod } 4$, which apparently is the same thing as $a^2 b^2 + (a')^2 (b')^2 - (a + a')^2 (b + b')^2 + 2a'b$.

Anyway, what I gotta understand first of all, is what it means by having the two last parameters for $\tilde {w}$ seperated by $;$ instead of an ordinary $,$.

That is: why $\tilde{w}(a, b ; a', b')$ instead of $\tidle{w}(a, b, a', b')$?

(Excuse me for the non-existant TeX markup btw, I couldn't seem to find any info about it in the post form.)

Edit: Updated the post with marked up equations, thanks for the pointer.

Last edited: Apr 20, 2006
2. Apr 19, 2006

### flybyme

Guess it is just semantics...

3. Apr 20, 2006