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January 23, 2018

CATEGORY: Questioning the Foundations Essay Contest (2012) [back]
TOPIC: Weaving Commutators: Beyond Fock Space by Michele Arzano [refresh]
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Author Michele Arzano wrote on Sep. 3, 2012 @ 13:45 GMT
Essay Abstract

The symmetrization postulate and the associated Bose/Fermi (anti)-commutators for field mode operators are among the pillars on which local quantum field theory lays its foundations. They ultimately determine the structure of Fock space and are closely connected with the local properties of the fields and with the action of symmetry generators on observables and states. We here show that the quantum field theory describing a relativistic particle coupled to three dimensional Einstein gravity as a topological defect must be constructed using a deformed algebra of creation and annihilation operators. This reflects a non-trivial group manifold structure of the classical momentum space and a modification of the Leibniz rule for the action of symmetry generators governed by Newton's constant. We outline various arguments suggesting that, at least at the qualitative level, these three-dimensional results could also apply to real four-dimensional world thus forcing us to re-think the ordinary multiparticle structure of quantum field theory and many of the fundamental aspects connected to it.

Author Bio

Dr. Arzano is a researcher in theoretical physics at the "Sapienza" University of Rome in Italy. He obtained his PhD from the University of North Carolina at Chapel Hill and has worked as a Postdoctoral Researcher at the Perimeter Institute for Theoretical Physics in Canada and as a Marie Curie Fellow at Institute for Theoretical Physics at Utrecht University, The Netherlands. Part of his current research revolves around the question of which of the fundamental pillars of our current description of high energy physics can or must be rethought when (quantum) gravity enters the picture.

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Alan Hutchinson wrote on Sep. 3, 2012 @ 21:17 GMT
This is serious stuff.

Arzano does not question the basic structure of QFT or GR.

If they are sound, and if his approach also works for 3 space dimemsions and 1 time dimension, then it suggests that QFT must be much more subtle than hitherto thought.

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Jonathan J. Dickau wrote on Sep. 4, 2012 @ 19:46 GMT
Yes indeed,

I agree that this is serious and interesting. It hovers near the limits of my Math comprehension, so is not easy reading for the Math challenged, but it kept my interest by continually coming back to comprehensible ideas.

I believe you effectively demonstrate that a deformed algebra is necessary, Michele, and it appears that your construction does the job nicely. I will need to re-read for details before I know for sure, but I find the derivation of a non-commutative rule to be a satisfying result.

all the best,


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Jonathan J. Dickau wrote on Sep. 4, 2012 @ 19:49 GMT
I meant to say;

When gravity enters the picture, we can no longer assume a 'level playing field' in terms of equal weighting, so it only makes sense that something like Dr. Arzano's prescription would be needed.



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M. Arzano wrote on Sep. 5, 2012 @ 14:34 GMT
Hi Alan and Jonathan,

Thanks for appreciating the message I try to convey in the essay. Your comments go exactly to the point: gravity and backreaction in certain specific regimes (might) require a simple yet non-trivial "deformation" of the very basic structures of ordinary local QFT. If we were able to identify a similar mechanism in 3+1 dimensions (as we are trying to) this would give much food for thought for everyone dealing with the puzzles of quantum field theory in curved spaces.

Best regards,


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Hoang cao Hai wrote on Sep. 19, 2012 @ 15:09 GMT

Very interesting to see your essay.

Perhaps all of us are convinced that: the choice of yourself is right!That of course is reasonable.

So may be we should work together to let's the consider clearly defined for the basis foundations theoretical as the most challenging with intellectual of all of us.

Why we do not try to start with a real challenge is very close and are the focus of interest of the human science: it is a matter of mass and grain Higg boson of the standard model.

Knowledge and belief reasoning of you will to express an opinion on this matter:

You have think that: the Mass is the expression of the impact force to material - so no impact force, we do not feel the Higg boson - similar to the case of no weight outside the Earth's atmosphere.

Does there need to be a particle with mass for everything have volume? If so, then why the mass of everything change when moving from the Earth to the Moon? Higg boson is lighter by the Moon's gravity is weaker than of Earth?

The LHC particle accelerator used to "Smashed" until "Ejected" Higg boson, but why only when the "Smashed" can see it,and when off then not see it ?

Can be "locked" Higg particles? so when "released" if we do not force to it by any the Force, how to know that it is "out" or not?

You are should be boldly to give a definition of weight that you think is right for us to enjoy, or oppose my opinion.

Because in the process of research, the value of "failure" or "success" is the similar with science. The purpose of a correct theory be must is without any a wrong point ?

Glad to see from you comments soon,because still have too many of the same problems.

Regards !


August 23, 2012 - 11:51 GMT on this essay contest.

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Member Olaf Dreyer wrote on Sep. 27, 2012 @ 12:56 GMT
Dear Michele:

Great essay. I like your "humble" attitude towards quantum gravity: Don't ask for the whole theory but look instead at the traces the theory might leave in our better known physics (local quantum field theory in this case).

The interesting question of course is whether the structure that you have described in 2+1 dimensions has a counterpart in 3+1 dimensions. In 2+1 dimensions particles appear in this very peculiar way as conical singularities. What is the situation in higher dimensions? Is it absolutely necessary to have this topological structure?

All the best.


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Member Benjamin F. Dribus wrote on Oct. 1, 2012 @ 19:58 GMT
Dear Michele,

I like this idea. I wonder what it would look like from a path-integral perspective? The modeling of particles as slight topological defects with simple properties seems like it might serve as a halfway house to a suitable “sum over geometries.” Take care,

Ben Dribus

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Sergey G Fedosin wrote on Oct. 4, 2012 @ 05:27 GMT
If you do not understand why your rating dropped down. As I found ratings in the contest are calculated in the next way. Suppose your rating is
was the quantity of people which gave you ratings. Then you have
of points. After it anyone give you
of points so you have
of points and
is the common quantity of the people which gave you ratings. At the same time you will have
of points. From here, if you want to be R2 > R1 there must be:
In other words if you want to increase rating of anyone you must give him more points
then the participant`s rating
was at the moment you rated him. From here it is seen that in the contest are special rules for ratings. And from here there are misunderstanding of some participants what is happened with their ratings. Moreover since community ratings are hided some participants do not sure how increase ratings of others and gives them maximum 10 points. But in the case the scale from 1 to 10 of points do not work, and some essays are overestimated and some essays are drop down. In my opinion it is a bad problem with this Contest rating process. I hope the FQXI community will change the rating process.

Sergey Fedosin

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Donatello Dolce wrote on Oct. 5, 2012 @ 13:59 GMT
Ciao Michele,

nice essay, I am using a similar formalism to generalize my theory to fermionic fields, by means of the analogies with twistors and zitterbewegung. See my essay .

Best regards,


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Jayakar Johnson Joseph wrote on Nov. 17, 2012 @ 16:15 GMT
Dear Michele Arzano,

Local fluctuations of the fields in quantum field theory expressional with degrees of freedom, is indicative of the elasticity of a string-segment described in Coherently-cyclic cluster-matter paradigm of universe.

The Fock space that describes the quantum states of a variable or unknown number of particles from a single particle Hilbert space is indicative of the probability of existence of string-segment of matter representational with multiple points in that segment in that quantization is expressional only with its dynamics as eigen-rotation that represents tetrahedral-brane. This implies that, ‘raison d'être’ of universe is the collective dynamics of string-matter continuum rather than space-time continuum, in that time and space emerges with the eigen-rotations of string-segments. As eigen-rotational phases of a cycle is not commutative, anticommutativity is applicable with this string-matter continuum scenario, in that negation of eigen-rotational chirality is descriptive in accordance with matter-antimatter asymmetry and thus the ‘Weaving Commutators’ postulate is applicable with this paradigm also.

With best wishes


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