An 8-dimensional realization of the Clifford algebra in the 5-dimensional Galilean space-time

Details An 8-dimensional realization of the Clifford algebra in the 5-dimensional Galilean space-time An 8-dimensional realization of the Clifford algebra in the 5-dimensional Galilean space-time

2007-10-30

arxiv.org/abs/0710.5556v1

J.Phys.A41:125402,2008

Physics

High Energy Physics

High Energy Physics - Theory

32 pages, no figure

Scientific paper

10.1088/1751-8113/41/12/125402

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

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