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arXiv · 0710.5556

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

M. Kobayashi·M. de Montigny·F. C. Khanna
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Abstract

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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M. Kobayashi, M. de Montigny, F. C. Khanna. 2007-10-30. An 8-dimensional realization of the Clifford algebra in the 5-dimensional Galilean space-time. https://doi.org/10.1088/1751-8113%2F41%2F12%2F125402

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