An eight-dimensional realization of the Clifford algebra in the five-dimensional Galilean covariant spacetime

We give an eight-dimensional realization of the Clifford algebra in the five-dimensional Galilean covariant spacetime by using a dimensional reduction from the (5 + 1) Minkowski spacetime to the (4 + 1) Minkowski spacetime which encompasses the Galilean covariant spacetime. A set of solutions of the Dirac-type equation in the five-dimensional Galilean covariant spacetime is obtained, based on the Pauli representation of 8 × 8 gamma matrices. In order to find an explicit solution, we diagonalize the Klein–Gordon divisor by using the Galilean boost.