Quantum Physical Origin of Lorentz Transformations
Résumé
Our aim is to derive the symmetries of the space-time, i.e. the Lorentz transformations, from discrete symmetries of the interactions between the most fundamental constituents of matter, in particular quarks and leptons. The role of Pauli’s exclusion principle in the derivation of the SL(2,C), symmetry is put forward as the source of the macroscopically observed Lorentz symmetry. Then Pauli’s principle is generalized for the case of the Z 3 grading replacing the usual Z 2 grading, leading to ternary commutation relations for quantum operator algebras. In the case of lowest dimension, with two generators only, it is shown how the cubic combinations Z 3-graded elements behave like Lorentz spinors, and the binary product of elements of this algebra with an element of the conjugate algebra behave like Lorentz vectors.