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Using post-Galilean space and time derivatives transformations and quantummechanics, we have found a new particle-wave equation besides the Klein-Gordonequation describing a spinless scalar particle. This new equation can also beobtained from Dirac's equation if $\beta=\gamma(1\pm\frac{v}{c})$. Biot-Savartlaw and additional continuity equations are obtained as a consequence of theinvariance of Dirac's equation and Maxwell's equations under thesetransformations.

Post-Galilean transformations of space and time derivatives and their consequences