What is your opinion of Linear Canonical Transformations?

  • #1

Summary:

a new alternative way for the unification of fundamental interactions ?
Hello everyone,

I looked for the best physics forum to ask this question because the subject interests me a lot. The authors of this preprint (https://arxiv.org/abs/1804.10053) seem to claim that their approach (using linear canonical transformations) is a new alternative way for the unification of fundamental interactions. So I would like to have your opinion on the matter. Thank you in advance
 

Answers and Replies

  • #2
strangerep
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They seem to use a naive relativistic version of the canonical commutation relations, yet seem unaware of Pauli's argument that this allows energy to be unbounded ##\mbox{below}^1##. They also seem unaware that Linear Canonical Transformations (LCTs) have been used for decades (albeit in a different form) as Bogoliubov transformations in condensed matter theory and QFT.

The 1st paper seems not to have been published in a peer-reviewed journal, and its only subsequent citations are from one or more of the original authors. Their next paper appears in the IJAMTP, which is one of the Science Publishing Group's journals. SPG have been criticised in the past for predatory practices.

For myself, I'm disinclined to spend any more than a few minutes on this work until after it gets published in a reputable peer-reviewed journal.

-------------
Note 1: To be fair, Galapon (and many others) have written extensively about Pauli's theorem and where/how it could be inapplicable. See, e.g., Galapon's 1999 article, and
citations thereto.
 
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  • #3
Thank you for your answer , it really helps me in analyzing it. However after reading your arguments, I read the paper again and it seems like your first and second arguments against them are not very fair if i can say that :)

1-"They seem to use a naive relativistic version of the canonical commutation relations, yet seem unaware of Pauli's argument that this allows energy to be unbounded below1"

If you read more carefully , you will see that they are aware about this ''time operator problem'' and they even give some recent references who adress it.

2-'' They also seem unaware that Linear Canonical Transformations (LCTs) have been used for decades (albeit in a different form) as Bogoliubov transformations in condensed matter theory and QFT. ''

I guess (for the debate...)that they probably know about the "Bogoliubov transformations" if they have learned QFT like anyone who has learned it seriously. But it looks like the difference is not negligible : In my knowledge (maybe i am wrong myself ) , Bogoliubov, for instance, never speak about a time operator or about mixing spacetime with energy-momentum like they do (i.e the two concepts are different from a physical point of view) and is there also the introduction of the integral transfoms or the pseudo-symplectic group in the framework of the Bogoliubov transformations?

Anyway, i would like to say thank you again for your reaction and answer. But as a researcher and scientist we must always have a critical thinking (as you did with their manuscript) and from my side, I also wanted to ''criticize'' your answer so that there is a real debate but not just a criticism against them :)
 
  • #4
strangerep
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However after reading your arguments, I read the paper again and it seems like your first and second arguments against them are not very fair if i can say that :)

1-"They seem to use a naive relativistic version of the canonical commutation relations, yet seem unaware of Pauli's argument that this allows energy to be unbounded below1"

If you read more carefully , you will see that they are aware about this ''time operator problem'' and they even give some recent references who adress it.
OK, they are aware of it, but (IMHO) don't deal with it satisfactorily. I have modified my post #2 accordingly to say that the references they quote appeal to various different methods to circumvent Pauli's argument, including Born reciprocity, discrete time, wave packet techniques, etc. These are not a single unified solution to the problem, hence leaves me unimpressed.

2-'' They also seem unaware that Linear Canonical Transformations (LCTs) have been used for decades (albeit in a different form) as Bogoliubov transformations in condensed matter theory and QFT. ''

[...], Bogoliubov, for instance, never speak about a time operator or about mixing spacetime with energy-momentum like they do (i.e the two concepts are different from a physical point of view)
Bogoliubov transformations, as usually written, involve mixing of annihilation and creation operators -- which is equivalent to mixing position and momentum operators.

Edit: Btw, their claim to obtain properties of fermions in the Standard Model seems to rely on using an unphysical 5D spacetime, if I'm reading their papers correctly -- including their other paper arXiv:1806.07228. If I'm reading them correctly, that's a red flag for me.
 
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  • #5
It is sounds like he's getting defensive. It sounds like he's trying to defend his own theory. I suspect the original poster wrote the paper himself, and he's pretending that somebody else wrote it to try to make it sound more credible. If you are really two different people, give more information about yourself, and more information about the other guy.
 
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  • #6
strangerep
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To be fair, the OP was right to ping me for initially not reading far enough into the paper before commenting on the Pauli theorem business.

I don't actually care about the identity of the OP. I only care about whether there's a high enough probability of those papers having enough scientific merit to justify spending my time studying them in gory detail.
 
  • #7
give more information about yourself, and more information about the other guy.
Thank you for your reaction. My goal is to have "objective opinions" on the scientific content of this preprint with a critical thinking. If people give opinion against it and i see that there are probably scientific flaws in these opinions, as a scientist and researcher, it is natural for me to identify and criticize it . But if people are going to defend this preprint and I also find flaws in their assertions, I would like to criticize them as well. My goal is to have "scientific opinion" and "scientific debate" on the content of this prepint. If you have any opinions in this framework they are welcome. But if you are interested in the "personal informations" of the authors I think you can contact them or do research about them on the net for instance.
 
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  • #8
Btw, their claim to obtain properties of fermions in the Standard Model seems to rely on using an unphysical 5D spacetime, if I'm reading their papers correctly -- including their other paper arXiv:1806.07228. If I'm reading them correctly, that's a red flag for me.
To my knowledge, pentadimensional theories have been around in physics for decades. There are even theories which use a spacetime having a dimension greater than 5. The de Sitter relativity, which is discussed in the preprint, for instance, have a pentadimensional background. But it is true that the "physical aspect" of these theories is still debatable.
 
  • #9
berkeman
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My goal is to have "scientific opinion" and "scientific debate" on the content of this prepint.
Please let us know when it has been published. We can continue the discussion then. We do not aid in the peer-review process. Thread is closed.
 
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