
#1
Feb412, 07:54 PM

P: 381

To people familiar with QFT. You know quantum fields are noninteracting and they use perturbations methods. Is there other studies or programme that would replace conventional QFT with full fledged interacting quantum fields?
Also about Second Quantization where they treat the KleinGorden and Dirac equations acting like classical equations like Maxwell Equations and quantize them to create field quantas such as matter or fermionic fields. Is there any studies or programme about alternative to this? Or are you certain 100% that Second Quantization is fully correct? And if QFT being not yet perfect due to the noninteracting fields for example. Why are physicists convinced they an arrive at the Theory Of Everything when the foundations are faulty... or maybe they are just contended for now to arrive at Quantum Gravity? And can one even reach it with a possibily faulty QFT foundations? Maybe there is no theory of quantum gravity precisely because QFT is faulty? How possible is this? 



#2
Feb512, 04:07 AM

P: 344

You impression of QFT is very inaccurate.




#3
Feb512, 04:43 AM

P: 381

http://www.amazon.com/StoryLightIn...8438503&sr=81 Which part of the following do you think is inaccurate and why? 



#4
Feb512, 04:50 AM

P: 3,015

Alternatives to QFT
So, where does he say matter fields are noninteracting?




#5
Feb512, 05:07 AM

Sci Advisor
P: 5,307

there are of course fully nonperturbative methods in QFT




#6
Feb512, 05:31 AM

P: 381

"A Fock space is constructed from the Hilbert space associated with the singleparticle theory. You use the singleparticle space to construct a space of 2particle states, a space of 3particle states, and so on, and then you combine them all into a Hilbert space that contains all the 1particle states, all the 2particle states, and so on. This Hilbert space is called a Fock space. So it's just an algebraic construction. You need nothing more than the Hilbert space from the singleparticle theory to define it, and the singleparticle theory can be defined using a Lagrangian with no products of more than two field components or derivatives of field components. However, in nonrigorous QFT, I think the idea is just to ignore that the interacting Hilbert space is really a different Hilbert space, and just introduce operators that can take nparticle states to (n+1)particle states for example. In this context, Fock space is, as you put it, "pretending to have interaction when it doesn't really". I really suck at QFT beyond the most basic stuff, so I can't explain it better, and I might even be wrong (about the stuff in this paragraph)." 



#7
Feb512, 05:41 AM

P: 3,015

In my opinion, the most important sentence in your post is the bolded one. If there are products of more than 2 field operators in the Lagrangian, then this is necessarily an interction. 



#8
Feb512, 06:44 AM

P: 381

What? Let's go to the context used by M.Y. Han book "A Story Of Light: A Short Introduction To Quantum Field Theory Of Quarks And Leptons". I'll quote only the relevant passages and omit the math and other detailing part: "The quantization of fields and the emergence of particles as quanta of the quantized fields discussed in Chapter 9 represent the very essence of quantum field theory. The fields mentioned so far  KleinGorden, electromagnetic as well as Dirac fields  are, however, only for the noninteracting cases, that is, for free fields devoid of any interactions, the forces. The theory of free fields by itself is devoid of any physical content: there is no such thing in the real world as a free, noninteracting electron that exerts no force on an adjacnet electron. The theory of free fields provides the foundations upon which one can build the framwork for introducing real physics, namely, the interaction among particles." [omitting 2 pages of calculations and details] "Quantum field theory for interacting particles would have been completely solved, and we could have moved beyond it. Well, not exactly. Not exactly, because no one can solve the highly nonlinear copuled equations for interacting fields that result from the interacting Lagrangian density obtained by the subtitution rule. Exact and analytical solutions for interacting fields have never been obtained: we ended up with the Lagrangian that we could not solve!" [omitting a page] "At this point, the quantum field theory of interacting particles proceeded towards the only other alternative left: when so justified, treat the interaction part of the Lagrangian as a small perturbatoin to the free part of the Lagrangian" [I won't quote other paragraphs anymore. Just see it in amazon free page preview if necessary] Do you know the part about "subtitution rule" he was talking about? Any relation to it that you are talking about? He basically said the subtitution rule couldn't be solved. And we are left only with perturbation, and we know it is seems ad hoc. Therefore Quantum Field Theory seems to be flawed. How then could they arrive at the right theory of Quantum Gravity with such a flawed foundation?! 



#9
Feb512, 07:51 AM

Sci Advisor
P: 8,000

For a simple analogy, a linear oscillator has sinusoidal oscillations.
A nonlinear oscillator does not have sinusoidal oscillations. Can the solution to the nonlinear oscillator be expressed as a sum of sinusoidal oscillations? Yes  that's what Fourier decomposition is. For QFT, the analogy is: linear > noninteracting nonlinear > interacting sinusoidal > Fock space. 



#10
Feb512, 07:59 AM

Sci Advisor
P: 5,307

The Fock space states are "blind" for interactions. The interactions are represented by
operators acting on Fock states. It's true that for some questions Fock states are not the best calculational tool, but they are not a foundational problem. 



#11
Feb512, 08:30 AM

P: 476

Only free fields are welldefined in QFT, but there is not a replacement for «fully fledged interacting quantum fields» because the concept of field is not defined there. ii) «Second Quantization» is a misnomer. There is nothing that is quantized twice as Weinberg often remarks. 'Second' quantization is a formalism for dealing with creating/destruction and creation/destruction is also used in ordinary QM. iii) Only some naive physicists as string (brane and M) theorists believed that they could obtain a «Theory Of Everything» over the basis of QFT. Others are working in more general theories, including far reaching generalizations of string, brane, and M theory. iv) The fiasco with quantum gravity has little to see with the limitations of QFT, and more with misunderstandings about general relativity. 



#12
Feb512, 08:41 AM

Sci Advisor
P: 5,307

 with a minor comment or question: is it really the concept of a "field" or a "field operator" that makes problems, or the concept for "interaction of fields". 



#13
Feb512, 10:09 AM

P: 3,015

Then, your last question is a false contradiction ( It is equivalent to the line of reasoning: 1. If we can arrive at Quantum Gravity with the current formalism, then we know the current formalism is correct. 2. QFT is part of the current formalism.  If we know the current formalism is correct, then we know QFT is correct. If we can arrive at QG with the current formalism, then QFT is correct. 3. QFT is incorrect.  We cannot arrive at QG with the current formalism. ) because premise 3 is the wrong conclusion that you drew from the above wrong analysis. Also, relating to my previous post, see tom.stoer's post #10: 



#14
Feb512, 04:59 PM

P: 476

String theorists were notorious for believing that GR is equivalent to a spin2 field theory over a flat background. And claimed that string theory was the final theory. String theorists did need about 40 years to understand that they would begin to search a backgroundless version (Mtheory), but no string theorist has serious ideas about what Mtheory is (M is somewhat used for Mistery). LQG community is also rather confused but in a somewhat complementary way. 



#15
Feb512, 05:45 PM

Sci Advisor
P: 5,307





#16
Feb512, 05:51 PM

P: 381

I learnt from M.Y. Han book that there are 3 phases of development of quantum field theory and how they deal with noninteracting fields. I'll summarize it.
First phase (Early 1950s)  Langrangian Field Theory  based on canonical quantization, success in QED followed by nonexpandability in the case of strong nuclear force and by nonrenomalizability in the case of weak nuclear force. Second phase (1950s1960s)  Axiomatic QFT  for example SMatrix theories and other axiomatic approaches, however they did not bring solutions to quantum field theories any closer than the Lagrangian field theories. Third phase (1970s)  (Lagrangian) gauge field theory  ongoing My question is. Can you make use of Gauge Theory without using Quantum Field Theory? Or the two completely related? But noether theorem can be applied to newtonian physics so can the gauge symmetry concept of electromagnetism U(1), electroweak U(1)xSU(2), Strong SU(3) can be developed without using the concept of quantum field theory? 



#17
Feb512, 09:35 PM

P: 3,015





#18
Feb512, 10:37 PM

Sci Advisor
P: 1,721




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