# Interpretation of Interaction in Boosts in QFT

1. Sep 14, 2009

### izh-21251

Question concerns the existence of the interaction in boost operator in the instant form of relativistic dynamics.
(referring to "Relativistic quantum dynamics" after E.V.Stefanovich, http://arxiv.org/abs/physics/0504062)

From the existance of interactions in boosts (e.g., in instant form of dynamics) it is possible to infer, that inertial transformations in quantum systems also carry dynamical character, i.e. depend on interactions.
In simpler words, the Lorentz-group transformations are only the approximations of tranformation laws for observables in INTERACTION-FREE regions.

Is there any prooved experimental evidence, that in interacting quantum systems (due to the presence of interaction in boost operators in Dirac's instant form) the Lorentz transformations laws do not hold?
Are there any ideas of at least theoretically feasible experiments, that can proove or refute this theory?

If (!) we adopt the idea of non-validity of Lorentz transformations in the interacting systems, this (as seems to me) will mean the end of conventional QFT.
This is simply because the new theory is no longer the compound of quantum mechanics and special relativity (ref. to "The quantum theory of fields" by S.Weinberg) and must no longer be called QFT.

No less vital question -- is it (even theoretically) possible to build such a theory -- the theory invariant under dynamical transformation group (instead of free one)??

_________________________________________________________
Thanks everybody answering my questions here!

2. Sep 14, 2009

### meopemuk

I just wanted to add that the dependence of the total boost operator on interactions is not an exotics, but a well-established fact:

P. A. M. Dirac, "Forms of relativistic dynamics", Rev. Mod. Phys. 21, (1949), 392.

"The quantum theory of fields" by S.Weinberg, section 3.3

If we accept that the boost operator is interaction-dependent (see above) and that in quantum mechanics velocity-induced transformations of observables are described by the application of the boost operator, then there is no other choice but to conclude that these velocity-induced transformations do depend on the presence of interactions, and that simple linear Lorentz transformation formulas of special relativity are merely approximations. Note also that the (Lorentz) group structure of these interaction-dependent transformations remains unaltered by the interaction.

No, there is no experimental evidence yet. The predicted effects are too small. The most promising approach is to observe the decay laws of fast-moving unstable particles:

E. V. Stefanovich, "Quantum effects in relativistic decays", Int. J. Theor. Phys. 35 (1996), 2539 ( http://www.geocities.com/meopemuk/IJTPpaper.html )

M. I. Shirokov, "Decay law of moving unstable particle", Int. J. Theor. Phys. 43 (2004), 1541.

M. I. Shirokov, "Evolution in time of moving unstable systems", Concepts of Physics, 3 (2006), 193 ( http://www.arxiv.org/abs/quant-ph/0508087 )

I believe you are not correct here. The "conventional QFT" is invariant under (what you call) the "dynamical transformation group". This is briefly mentioned in Weinberg's book. The full proof of the relativistic invariance of QED (with interaction-dependent boosts) can be found in Appendix B of

S. Weinberg, "Photons and gravitons in perturbation theory: Derivation of Maxwell's and Einstein's equations", Phys. Rev. 138 (1965), B988.