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We extend the 5-dimensional Galilean space-time to a (5+1) Galileanspace-time in order to define a parity transformation in a covariant manner.This allows us to discuss the discrete symmetries in the Galilean space-time,which is embedded in the (5+1) Minkowski space-time. We discuss the Dirac-typefield, for which we give the 8\times 8 gamma matrices explicitly. Wedemonstrate that the CPT theorem holds in the (5+1) Galilean space-time.

CPT theorem in a (5+1) Galilean space-time