We modify a Lie algebra expansion method recently introduced for the (2 + 1)dimensional kinematical algebras so as to work for higher dimensions. This new improved and geometrical procedure is applied to expanding the (3 + 1)-dimensional Galilei algebra and leads to its physically meaningful ‘expanded’ neighbours. One expansion gives rise to the Poincaré algebra, introducing a curvature −1/c in...

The energy and time variables of the elementary classical dynami-cal systems are described geometrically, as canonically conjugate coordinates of an extended phase-space. It is shown that the Galilei action of the inertial equivalence group on this space is canonical, but not Hamiltonian equivari-ant. Although it has no effect at classical level, the lack of equivariance makes the Galilei actio...

The energy and time variables of the elementary classical dynami-cal systems are described geometrically, as canonically conjugate coordinates of an extended phase-space. It is shown that the Galilei action of the inertial equivalence group on this space is canonical, but not Hamiltonian equivari-ant. Although it has no effect at classical level, the lack of equivariance makes the Galilei actio...

By means of the generalized Galilei covariant EM field equations, the EM potentials and EM fields of a charged particle moving with an arbitrary nonuniform velocity v(t) in an inertial frame with substratum flow w are calculated. It is shown that the dynamic EM fields are excitations of the EM ether caused by the motion v(t) — w of the charge relative to the wave carrier with velocity w. Qualit...

A method to develop physical theories of free particles in spacetime with the Galilean metric is presented. The method is based on a Principle of Analyticity and a Principle of Relativity, and uses the Galilei group of the metric. The first principle requires that state functions describing the particles are analytic and the second principle demands that dynamical equations for these functions ...

The maximal invariance group of Newton's equations for a free nonrelativistic point particle is shown to be larger than the Galilei group. It is a semi-direct product of the static (nine-parameter) Galilei group and an SL(2, R) group containing time-translations, dilations and a one-parameter group of time-dependent scalings called expansions. This group was first discovered by Niederer in the ...

The energy and time variables of the elementary classical dynami-cal systems are described geometrically, as canonically conjugate coordinates of an extended phase-space. It is shown that the Galilei action of the inertial equivalence group on this space is canonical, but not Hamiltonian equivari-ant. Although it has no effect at classical level, the lack of equivariance makes the Galilei actio...

The maximal invariance group of Newton's equations for a free non-relativistic point particle is shown to be larger than the Galilei group. It is a semi-direct product of the static (nine-parameter) Galilei group and an SL(2, R) group containing time-translations, dilations and a one-parameter group of time-dependent scalings called expansions. This group was first discovered by Niederer in the...