How we can improve QFT?
Here we discussed that QFT in its current form cannot describe the time evolution of wave functions and observables. Here we quoted Weinberg as saying that QFT is the only way to unify relativity with cluster separability and that any fundamental theory in the low-energy limit should look like QFT. So, what shall we do now? Give up? No.
It appears that Weinberg's profesy is wrong. There is a way to construct a low-energy fundamental relativistic quantum theory that does not look like QFT. Examples of such theories were constructed by Kita in [1] and in several later papers. Similar ideas were explored by Kazes [2]. By following these approaches, one can define interaction operators in H = H_0 + V and K = K_0 + W (see here ) so that (i) the Poincare commutators are satisfied, (ii) the interaction operators are cluster separable, (iii) V and W yield zero when acting on the vacuum and 1-particle states. The last condition is important to have a well-defined time evolution in the theory.
The bad news about Kita's theory is that he was able to construct only simple models that apparently have no counterparts in nature. The good news is that his approach can be applied to realistic theories, such as QED. A satisfactory version of QED with properties (i), (ii), and (iii) can be constructed by using the "dressed particle" approach. More about that in another posting.
[1] H. Kita, "A non-trivial example of a relativistic quantum theory of particles without divergence difficulties", Progr. Theor. Phys., 35, (1966) 934.
[2] E. Kazes, "Analytic theory of relativistic interactions", Phys. Rev. D, 4, (1971) 999.
It appears that Weinberg's profesy is wrong. There is a way to construct a low-energy fundamental relativistic quantum theory that does not look like QFT. Examples of such theories were constructed by Kita in [1] and in several later papers. Similar ideas were explored by Kazes [2]. By following these approaches, one can define interaction operators in H = H_0 + V and K = K_0 + W (see here ) so that (i) the Poincare commutators are satisfied, (ii) the interaction operators are cluster separable, (iii) V and W yield zero when acting on the vacuum and 1-particle states. The last condition is important to have a well-defined time evolution in the theory.
The bad news about Kita's theory is that he was able to construct only simple models that apparently have no counterparts in nature. The good news is that his approach can be applied to realistic theories, such as QED. A satisfactory version of QED with properties (i), (ii), and (iii) can be constructed by using the "dressed particle" approach. More about that in another posting.
[1] H. Kita, "A non-trivial example of a relativistic quantum theory of particles without divergence difficulties", Progr. Theor. Phys., 35, (1966) 934.
[2] E. Kazes, "Analytic theory of relativistic interactions", Phys. Rev. D, 4, (1971) 999.
posted by Eugene Stefanovich at 11:26 PM
1 Comments:
Improve it by finding a full causal dynamics representation for the best verified quantum field theory, the Yang-Mills Standard Model!
For example, the exchange radiation causing forces should be quantified and represented by a dynamic model.
The physical reasons for the renormalization cutoffs required should be explained in causal terms by a model which can then itself be checked via making predictions that can be tested.
The key thing about renormalization is that the polarized vacuum around a particle cancels out most of the core charge, but not all of it.
Why doesn't the vacuum polarize enough to completely cancel out charges?
I don't think the creation-annihilation operators are clearly understood in quantum field theory.
What seems to be the case is that the strong field near a charge actually cause the virtual vacuum charges, as well as polarizing them. Because of the way the abundance of virtual charges in the vacuum falls off with distance from the real charge core, there is a limit to the amount of cancelation by polarization, so some charge continues to be seen even at long distances.
This is different from Dirac's sea, in which the entire vacuum is full of virtual charge.
So I think renormalized QFT indicates that the virtual charges of the vacuum are confined very close to the real charges, and don't extend everywhere.
This brings up the electroweak symmetry breaking problem. As I understand it, at low energy the vacuum attenuates 3 out of the 4 electroweak gauge bosons, by giving them mass (W+, Z-, Zo).
The mass breaks the symmetry, since the photon is a massless version of the Zo. This indicates that the Zo is a very important particle to study, being the massive partner of the photon.
Above electroweak unification energy, the mass causing agent (Higgs field?) dissociates from the electroweak gauge bosons, so symmetry is restored and all the gauge bosons then have infinite range.
Physically what this means is that, at high energy, things interact with a massive energy compared to the binding energy between charges and masses (Higgs particles or whatever).
Hence, the masses cease to dominate the electroweak charged gauge bosons.
Again, this raises the question what happens to the neutral but massive gauge boson Zo?
That is the key to everything. Why does it have mass?
If you look at its mass, it is very interesting. Multiply Zo mass by alpha/(2Pi), and you get 105.7 MeV, the muon mass.
Multiply Zo mass by (alpha)^2 /(2Pi) and you get 0.51 MeV, electron mass.
Finally, multiply Zo mass by n(N+1)(alpha)/(6Pi), where n is the number of real charges in close proximity (sharing the same electroweak polarized vacuum veil, eg n = 1 for leptons, n = 3 quarks for nucleons) and N is an integer.
This formula predicts quantized masses of all particles! You can test statistically and find that the data fits this formula well.
For the QFT physical mechanism behind these formula see:
http://electrogravity.blogspot.com/2006/06/more-on-polarization-of-vacuum-and.html
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