1999/09/02 by Francisco J. Herranz, Herranz, Francisco J., Mariano Santander +1
Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Group Theory (math.GR) #Mathematical Physics (math-ph) #Rings and Algebras (math.RA) #gr-qc #math-ph #math.GR #math.MP #math.RA
paper · pdf · doi:10.48550/arxiv.math-ph/9909005
14 pages, LaTeX. The expansion method is clarified
arxiv created 2000/10/09 · arxiv updated 2009/11/30
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 Poincare algebra, introducing a curvature -1/c2 in the flat Galilean space of worldlines, while keeping a flat spacetime which changes from absolute to relative time in the process. This formally reverses, at a Lie algebra level, the well known non-relativistic contraction c→ ∞ that goes from the Poincare group to the Galilei one; this expansion is done in an explicit constructive way. The other possible expansion leads to the Newton-Hooke algebras, endowing with a non-zero spacetime curvature ± 1/τ2 the spacetime, while keeping a flat space of worldlines.