Abstract
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.
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Barducci, A., Casalbuoni, R. & Gomis, J. A particle model with extra dimensions from coadjoint Poincaré symmetry. J. High Energ. Phys. 2020, 92 (2020). https://doi.org/10.1007/JHEP08(2020)092
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DOI: https://doi.org/10.1007/JHEP08(2020)092