The claim found in many textbooks that the Dirac equation cannot be written solely in terms of Pauli
matrices is shown to not be completely true. It is only true as long as the term ##IMG##
[http://ej.iop.org/images/0143-0807/37/5/055407/ejpaa2c9bieqn1.gif] {$\beta \psi $} in the usual
Dirac factorization of the Klein–Gordon equation is assumed to be the product of a square matrix β
and a column matrix ψ . In this paper we show that there is another possibility besides this matrix
product, in fact a possibility involving a matrix operation, and show that it leads to another
possible expression for the Dirac equation. We show that, behind this other possible factorization
is the formalism of the Clifford algebra of physical space. We exploit this fact, and discuss
several different aspects of Dirac theory using this formalism. In particular, we show that there
are four different possible sets of definitions for the parity, time reversal, and cha…