Galilean transformation

The Galilean transformationusedtransform betweencoordinatestwo coordinate systemsconstant relative motionNewtonian physics. The equations below, although apparently obvious, break down at speeds that approachspeedlight.

UnlikeGalilean transformation,relativistic Lorentz transformations can be shownapply at all velocities so far measured, andGalilean transformation can be regarded as low-velocity approximations toLorenz transformation.

UnderErlanger program,space-time (no longer spacetime)nonrelativistic physicsdescribed bysymmetry group generated by Galilean transformations, spacialtime translationsrotations.

Central extension ofGalilean group

1. The Galilean group: Here, we will only look at its Lie algebra. It's easyextendresults toLie group. The Lie algebraLspanned by E, P_i, C_iL_ij (antisymmetric tensor) subject

We can now give itcentral extension intoLie algebra spanned by E', P'_i, C'_i, L'_ij (antisymmetric tensor), M such that M commuteseverything (i.e. lies incenter, that's why it's calledcentral extension) and