Some readers think that I am “against” QED and QFT results because I am against renormalizations. I think I might be insufficiently clear in my critics of renormalizations and thus produced such a false impression.

No, on the contrary, the final results of QED are right and I use them as a valuable data. I am just for a short-cut to these results. A careful reader can easily infer my position from my posts. I am convinced that we (I mean the QED fathers and followers) work with a wrong QED Hamiltonian. Because of this, we are forced to “repair” the calculation results “on the go”. “Repairing” includes discarding unnecessary corrections to the fundamental constants and a selective summation of soft diagrams to all orders. So we only obtain the right inclusive cross sections in the end, not before!

The right Hamiltonian can give the same final results directly, in a routine perturbative way, without discarding any corrections and without summation of divergent diagrams to all orders. The right Hamiltonian, if you like, can be equally called an “exactly renormalized” Hamiltonian. It contains only physical characteristics and it must be constructed just in a more physical way – what is coupled permanently in nature should be implemented so in the new Hamiltonian rather than “coupled perturbatively”. A better initial approximation leads to a better perturbative series – the latter turns into finite and reasonably small corrections due to the new initial approximation being closer to the exact solution. That’s it!

Some readers want me to produce QED results with even more precision than the actual QED provides. They say it is the only way to attract attention to my approach. Frankly, they want too much from me (I mean, from one person). A theory development is a result of years of work of many professional researchers. And I do not even hold an academic position with sufficient research freedom to carry our these laborious calculations. So my results are modest in this respect. But I hope I outline the right direction quite unambiguously.

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I think this is a very clear description of what you are doing. One of the things I’m particularly interested in are the masses of the elementary particles. Since these are modified by renormalization, it would be nice for you to say how these are changed.

For example, one of the odd features of Koide’s equation for the lepton masses is that it works before renormalization of the lepton masses. See http://arxiv.org/abs/hep-ph/0506247 for further. Anyway, if reformulation is a way of avoiding having to change the (relative) masses of the charged leptons, this would give a theoretical explanation for why Koide’s mass equation does not deal with “bare” masses.

No mass is modified by the mass renormalization. On the contrary, the mass renormalization forces the “calculated” mass to be the same and equal to the experimental value. It is achieved with simple discarding perturbative correction to the original physical mass. The problem with it is that the renormalization prescription is not often represented as discarding corrections to a fundamental physical constant but as “absorbing” those corrections “into” the “bare” constant. Technically it is implemented as a subtraction of unnecessary corrections from the “calculated” constant, so it is just discarding and nothing else.

Fundamental constants are not calculable quantities by definition; that is why one is obliged to “redefine” them each time when they get “perturbative corrections”. The latter feature is due to our bad Lagrangian rather than because of physical effects (“screening” bare charge with bare virtual particles).

So my proposal is to advance a better, more physical Lagrangian and then the perturbative corrections to solutions will be small and never reducible, even partially, to corrections to the fundamental constants.

According to my understanding of interactions, the experimental masses belong to compound systems, and the theory should be constructed with such their meaning. In my opinion, the desired Lagrangian is not very different technically from the current “bare” Lagrangian, so you may safely work with the experimental masses. No other values are involved in the current (with renormalizations) and will not be involved in the future (without renormalizations) calculations.

Another thing I’d like to add is that renormalization itself can give modify a finite calculation to give a different finite result. From your post I believe that you are completely at ease with this.

What I’m doing is renormalization over finite dimensional spaces. These are always finite.

December 31, 2010 at 09:42 |

Dear Vladimir,

I think this is a very clear description of what you are doing. One of the things I’m particularly interested in are the masses of the elementary particles. Since these are modified by renormalization, it would be nice for you to say how these are changed.

For example, one of the odd features of Koide’s equation for the lepton masses is that it works before renormalization of the lepton masses. See http://arxiv.org/abs/hep-ph/0506247 for further. Anyway, if reformulation is a way of avoiding having to change the (relative) masses of the charged leptons, this would give a theoretical explanation for why Koide’s mass equation does not deal with “bare” masses.

January 1, 2011 at 12:38 |

Dear Carl,

No mass is modified by the mass renormalization. On the contrary, the mass renormalization forces the “calculated” mass to be the same and equal to the experimental value. It is achieved with simple discarding perturbative correction to the original physical mass. The problem with it is that the renormalization prescription is not often represented as discarding corrections to a fundamental physical constant but as “absorbing” those corrections “into” the “bare” constant. Technically it is implemented as a subtraction of unnecessary corrections from the “calculated” constant, so it is just discarding and nothing else.

Fundamental constants are not calculable quantities by definition; that is why one is obliged to “redefine” them each time when they get “perturbative corrections”. The latter feature is due to our bad Lagrangian rather than because of physical effects (“screening” bare charge with bare virtual particles).

So my proposal is to advance a better, more physical Lagrangian and then the perturbative corrections to solutions will be small and never reducible, even partially, to corrections to the fundamental constants.

According to my understanding of interactions, the experimental masses belong to compound systems, and the theory should be constructed with such their meaning. In my opinion, the desired Lagrangian is not very different technically from the current “bare” Lagrangian, so you may safely work with the experimental masses. No other values are involved in the current (with renormalizations) and will not be involved in the future (without renormalizations) calculations.

February 23, 2011 at 02:06 |

Another thing I’d like to add is that renormalization itself can give modify a finite calculation to give a different finite result. From your post I believe that you are completely at ease with this.

What I’m doing is renormalization over finite dimensional spaces. These are always finite.