This section provides a brief treatment of the Dirac wave equation, demonstrating its association with a particle of spin $\frac{1}{2}$ and positive mass $m$. It introduces the Minkowski-Clifford algebra, where the gamma matrices $\gamma(x)$ are defined for each $x \in \mathbb{R}^4$. These matrices generate a Clifford algebra over $\mathbb{R}^4$ with respect to the Lorentz scalar product. The map $\tau$ is an isomorphism from SL(2, $\mathfrak{C}$) to the spin group Spin(3,1), and it satisfies the commutative diagram involving the covering map $\sigma$. This leads to the relation $\gamma(A x) = \tau(A) \gamma(x) \tau(A)^{-1}$ for $x \in \mathbb{R}^4$ and $A \in \mathrm{SL}(2, \mathfrak{C})$. Additionally, the section defines the Dirac bundle $\xi_{\tau}^{\chi}$, which is associated with the restriction of the representation $\tau$ to $\mathrm{SU}(2)$, with fiber $\mathbb{C}^4$.This section provides a brief treatment of the Dirac wave equation, demonstrating its association with a particle of spin $\frac{1}{2}$ and positive mass $m$. It introduces the Minkowski-Clifford algebra, where the gamma matrices $\gamma(x)$ are defined for each $x \in \mathbb{R}^4$. These matrices generate a Clifford algebra over $\mathbb{R}^4$ with respect to the Lorentz scalar product. The map $\tau$ is an isomorphism from SL(2, $\mathfrak{C}$) to the spin group Spin(3,1), and it satisfies the commutative diagram involving the covering map $\sigma$. This leads to the relation $\gamma(A x) = \tau(A) \gamma(x) \tau(A)^{-1}$ for $x \in \mathbb{R}^4$ and $A \in \mathrm{SL}(2, \mathfrak{C})$. Additionally, the section defines the Dirac bundle $\xi_{\tau}^{\chi}$, which is associated with the restriction of the representation $\tau$ to $\mathrm{SU}(2)$, with fiber $\mathbb{C}^4$.