In quantum mechanics, free particles are running waves, and extended objects consist of standing waves.

Feynman proposed to solve the problem by inventing Feynman diagrams for running waves, and by suggesting harmonic oscillator wave functions for standing waves inside the particle.

However, Feynman and his coworkers did not use correct mathematics to satisfy all the known physical laws of quantum mechanics and special relativity. Is it possible possible to correct their mathematical errors?

In 1939, Wigner published a paper on the subgroups of the Lorentz group whose transformations leave the four-momentum of a given particle invariant. This subgroup is called Wigner's little group.

Thus, Feynman's oscillator wave functions should satisfy the symmetry of Wigner's little group. There are many review papers on this subject. You man look at a paper entitled

Since Wigner's little groups are subgroups of the Lorentz group, Einstein prevails both insider and outside the particle.

How about quantum mechanics inside and outside the moving extended particle?