Reflections on the evolution of physical theories

Conclusion

Let me come back to the successes of the Poincaré group in particle physics. This is a group with ten generators. The translation generators are responsible for the energy-momentum conservation laws, the rotation generators of the conservation of angular momentum, and the boost generators of the conservation ofinitial position. If positions are slightly different from the ones described by Minkowski space, it means that we have to change slightly the notion of boosts. If we remember that boosts were questionable in Minkowski space (see Section 9), we are not surprised. We are naturally led to a deformation of the Poincaré group which would preserve translations and rotations [such a deformation has been proposed by Lukierskiet al. (n.d.)]. By duality, small changes at short distances must correspond to small changes in large momenta. The fact that cutoffs for momenta are involved in QED is perhaps related to a noncommutative structure for our space. With such a structure, making the size of an electron go to zero is meaningless and consequently the difficulty of an electron with infinite energy also becomes meaningless. A noncommutative space is probably a way to solve the difficulties mentioned in the epigraphs to this paper.