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.

Download Essay PDF File

  • [deleted]

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.

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,

Jonathan

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.

Regards,

Jonathan

  • [deleted]

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,

Michele

22 days later

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.

Olaf

4 days later

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

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 [math]R_1 [/math] and [math]N_1 [/math] was the quantity of people which gave you ratings. Then you have [math]S_1=R_1 N_1 [/math] of points. After it anyone give you [math]dS [/math] of points so you have [math]S_2=S_1+ dS [/math] of points and [math]N_2=N_1+1 [/math] is the common quantity of the people which gave you ratings. At the same time you will have [math]S_2=R_2 N_2 [/math] of points. From here, if you want to be R2 > R1 there must be: [math]S_2/ N_2>S_1/ N_1 [/math] or [math] (S_1+ dS) / (N_1+1) >S_1/ N_1 [/math] or [math] dS >S_1/ N_1 =R_1[/math] In other words if you want to increase rating of anyone you must give him more points [math]dS [/math] then the participant`s rating [math]R_1 [/math] 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

  • [deleted]

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 http://fqxi.org/community/forum/topic/1503 .

Best regards,

Donatello

a month later

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'ĂȘtre' 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

Jayakar

Write a Reply...