Algorithmic and Axiomatic Approaches to the Construction of Quantum Field Theory

[Jacques]

I found this article and found it very interesting.

Abstract

Two possibilities of the quantum theory construction, indicated by Feynman, are examined. The

special features of the structure of the Standard Model (SМ) are enumerated, which attest to the

fact that SM is not an axiomatic, but an algorithmic theory. Deficiencies of SM and possibilities of

overcoming these deficiencies are indicated. The structure of the nonlinear quantum field theory

(NQFT) as an axiomatic theory, which makes it possible to overcome deficiencies in the Standard

Model, is presented.

 

My humble opinion is that it is better to have an axiomatic approach in science, but I don't know much about quantum theories.

Is it true that the Standard Model use a "Babylonian" approach ?

Does the maths in the article correct, or is it a word salad ?

 

I would like to have your opinion and comment on that article.

 

thanks

[timo]

My comments on the article are:

1) "published" in "Prespace Journal".

2) Factors of "[math]\frac{1}{4 \neq}[/math]" that are presumably meant to be "[math]\frac{1}{4 \pi}[/math]"

3) Many quotations from famous physicists. Interesting references section.

4) You can find many more articles of the same author on viXra.

[Jacques]

Thanks timo for your answers.

1) "published" in "Prespace Journal"

Do you mean that it is not a reliable source ?

Same question about viXra ?

[ajb]

I have not read the article. Constructive field theory in whatever guise is usually very formal and not really able to handle realistic theories. At some level they reduce to understanding the Wightman axioms. In particular, dealing with scalar field theory is hard enough, and though it can give hints about gauge theories the situation is far from clear.

 

Probably the best established approach is Haag and Kastler's algebraic quantum field theory. This has had some success, notably in understanding superselection rules and quantum field theory on non-hyperbolic space-times. I warn you the set up is very mathematical and based on c*-algebras.

 

Other approaches to constructive field theory often rely on some quite heavy analysis, understanding the operator product expansion or other algebraic constructions.

 

I am far from an expert in this area, but recommend the following

 

Haag, Rudolf (1992). Local Quantum Physics: Fields, Particles, Algebras. Springer.

 

R. F. Streater and A. S. Wightman, PCT, Spin and Statistics and All That, Princeton University Press, Landmarks in Mathematics and Physics, 2000. (actually a much older book than this)

 

John C. Baez, Irving E. Segal and Zhengfang Zhou. Introduction to Algebraic and Constructive Quantum Field Theory, Princeton University Press, 1992. Online here.

[timo]

Do you mean that [Prespace Journal] is not a reliable source? Same question about viXra?

That depends what you consider a "reliable source". I have no doubt about the source's reliability when it comes to asking if the person mentioned as the author actually exists and if he actually wrote the article himself. I also have no doubt that the author actually is serious about what he writes. So in that sense the source is reliable. For me, a quick look at the homepage of "Prespacetime Journal" ("about" section (edit: it did not seem to work when I tried, but now it seems it actually does), the "editorial board", ... come on, already the name of the journal sounds like "crackpot inside") tells me that I won't bother reading any of their "publications". But you are of course completely free to judge otherwise. In the end, I can not say anything against the content of the paper you dug up (since I didn't read it ).

Edited November 24, 2011 by timo

[Jacques]

AJB

I have not read the article

timo

In the end, I can not say anything against the content of the paper you dug up (since I didn't read it ).

OK...

I was hoping some real answer.

Edited November 25, 2011 by Jacques

[timo]

But with already 530 posts on sfn you should know well enough that you shouldn't expect one

[Jacques]

timo

Most of the time, people here reply , but I must admit that often replies goes of topic.

Here it is my lack of knowledge about the math in the article that motivated me to post. I thaught that someone who knows the quantum math would give me an appretiation of the validity of what is writen. I find that article and other articles by this author important if it can give a new perspective to quantum physic. I find fascinating the thaught that an electron can be describe as a rotating semi-photon. He use the same math and equation as the standard model, but give some sense to quantum physic.

Anyway, if somebody can review and tell me if it is good or not, thanks