Post-Galilean transformations and their consequences

Abstract

Using post-Galilean space and time derivatives transformations and quantum
mechanics, we have found a new particle-wave equation besides the Klein-Gordon equation
describing a spinless scalar particle. This new equation can also be obtained from Dirac’s
equation if β = γ

1 ±
v
c
. Biot-Savart law and additional continuity equations are obtained
as a consequence of the invariance of Dirac’s equation and Maxwell’s equations under these
transformations.