# Why isn't the ${\gamma}^5$ matrix called ${\gamma}^4$?

This is not really a physical question, but it relates to notation in QED.

The ${\gamma}^5$ matrix is defined as

$${\gamma}^5=i{\gamma}^0 {\gamma}^1{\gamma}^2{\gamma}^3$$

Wouldn't it be more logical to write ${\gamma}^5$ as ${\gamma}^4$?

Although $$\gamma ^{5}$$ uses the letter gamma, it is not one of the gamma matrices of Cl1,3(R). The number 5 is a relic of old notation in which $$\gamma ^{0}$$ was called "$$\gamma ^{4}$$".