Relativistic quantum theory of interacting particles

[meopemuk]

So, then, you have not proven relativistic covariance exactly, have you?

This is correct. The whole approach in Appendix O is perturbative and expansion in powers of 1/c^2 was used. Only low-order terms were retained in the proof.

However, there is a good reason to believe that relativistic invariance will be valid in higher orders as well. The traditional field-based QED is relativistically invariant (see Appendix N). The dressed particle approach is obtained from QED by means of a unitary dressing transformation, which preserves Poincare commutators (see subsection 10.2.8). Therefore, the full interaction potential between dressed charged particles must be relativistically invariant as well. Unfortunately, this full non-perturbative potential is not known yet and explicit proof of its invariance is not possible.

Eugene.

 

[Dickfore]

This is correct. The whole approach in Appendix O is perturbative and expansion in powers of 1/c^2 was used. Only low-order terms were retained in the proof.

However, there is a good reason to believe that relativistic invariance will be valid in higher orders as well.
Eugene.

lol, this is not considered a scientific argument. Why don't you derive a Hamiltonian in the next order in perturbation theory?

 

[meopemuk]

Why don't you derive a Hamiltonian in the next order in perturbation theory?

This is exactly what I'm doing right now. The calculations are rather non-trivial as they involve loop integrals with their ultraviolet and infrared divergences. If I'm successful I'll have radiative corrections to the Darwin-Breit Hamiltonian, which describe, e.g., the anomalous magnetic moment of the electron and the Lamb shift. I will be happy to report my findings here when I'm done.

Eugene.