2020/06/21 by Andrea Barducci, Roberto Casalbuoni, Barducci, Andrea +3
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #hep-th
paper · pdf · doi:10.48550/arxiv.2006.11725
14 pages
arxiv created 2020/06/21 · arxiv updated 2020/06/23
Starting from the coadjoint Poincaré algebra we construct a point particle relativistic model with an interpretation in terms of extra-dimensional variables. The starting coadjoint Poincaré algebra is able to induce a mechanism of dimensional reduction between the usual coordinates of the Minkowski space and the extra-dimensional variables which turn out to form an antisymmetric tensor under the Lorentz group. Analysing the dynamics of this model, we find that, in a particular limit, it is possible to integrate out the extra variables and determine their effect on the dynamics of the material point in the usual space time. The model describes a particle in D dimensions subject to a harmonic motion when one of the parameters of the model is negative. The result can be interpreted as a modification to the flat Minkowski metric with non trivial Riemann, Ricci tensors and scalar curvature