Talk:Fermion doubling

Complete rewrite

The article is a very important one in lattice field theory, so it deserves a good article about it. The rewrite is quite comprehensive, having compiled all views on the subjects taken on the subjects from the existing lattice QCD textbooks, especially Gattringer et al, Rothe, DeGrand et al, Monvay et al, as well as some relevant textbooks and papers. The article now covers fermion doubling in the naïve theory through three different methods: the doubling symmetry, the propagator poles, and the dispersion relation. It also gives the main solutions to the problem as well as the less well known point about derivative discretizations (mainly coming from Rothe's textbook). Also I have no idea why the article was a C-class before, but I do think it should be a C-class article now since it is comprehensive, well sourced, and (I hope) well written. OpenScience709 (talk) 19:47, 1 April 2022 (UTC)

Symmetric mass generation

I am concerned with the recent edits to do with Symmetric Mass Generation (SMG). They seem to have been primarily created by Yi-Zhuang You (as user:EverettYou) and IP editor 65.112.8.21, which represent an obvious conflict of interest, leading to an undue focus on it in this article. It is also a very recent idea that should not be overly emphasized with a paragraph in the "resolutions on fermion doubling" section compared to the others.

Wikipedia also does not function on the idea that a section should have ALL citations associated with the topic; the citations are mainly supposed to back up any claims made (so a single claim does not require 7 citations for example). Citations also sometimes serve the dual purpose of showing which particular paper the original idea came from, hence why I advocate for citing the original paper for a particular concept.

SMG does not deserve a paragraph to describe it; the first sentence suffices in this article so I suggest deleting the rest. Currently it has almost 1/3rd of all citations in this article, which is way too many concidering that it is a recent concept that forms a tiny aspect of the article. All it needs is 1 or 2 of the original papers that proposed this concept (whichever papers that may be? SMG seems to have been proposed in the 2018 papers, but it would be better to cite the papers that proposed it in a lattice setting to resolve fermion doubling; could the experts on this topic please let me know which papers did this?) to back up the first sentence claim. Again, I'm still super concerned that these other papers cited are all by the same two authors who made these edits, representing a conflict of interest.

EverettYou and IP 65.112.8.21: we should discuss this here to reach a consensus. Any counter arguments in line with Wikipedia Manual of Style are welcomed. OpenScience709 (talk) 10:21, 21 March 2023 (UTC)

indeed, the article is now very much unbalanced; a brief mention of SMG should be sufficient Brienanni (talk) 14:48, 21 March 2023 (UTC)

So I had a response to my points on my talk page. I propose continuing the discussion here.

Ok, let's work on this together. But first some comments.

The article is about fermion doubling, not about various realizations of fermions on the lattice, so we do not want to go into details of the formulation. Only how the formulation overcomes the Niesen-Ninomiya theorem. I think I'm fine with adding one or two additional sentences on this for each of the fermion realizations.

One crucial thing to do however is focus on the following BEFORE the SMG fermion: domain wall fermion, Ginsparg–Wilson fermion, overlap fermion, staggered fermion, twisted mass fermion, Wilson fermion. These are much more important and notable than SMG and the absence of a description of them but SMG having one will give the reader the wrong impression about SMG's importance.

I would also reduce the number of citations, for which I need your help. Wikipedia is not a scientific literature review which is trying to cite every relevant paper to a topic. It only cites what it talks about in the text. So, lets go through this:

• "goes beyond the fermion-bilinear model and introduces non-perturbative interaction effects": Give me 1-2 papers that explain what SMG on the lattice is (and/or the first paper to describe it) so we can cite that here.
• "Eichten-Preskill model": I'm happy with including this citation.
• ", which has been realized in explicit lattice models." Not sure that this last comment is necessary; it's going into details of the fermion lattice model itself rather than just describing how it overcomes fermion doubling. I think it should be implicit that these proposals work, otherwise they should not be in this article in the first place.
• As for Wang; Wen (2013). Wang; Wen (2019). Zeng; Zhu; Wang; You (2022): Not all of these are relevant, we only need to include the one that proposed the Eichten-Preskill model spinoff (2013 paper?). Maybe we can also inlcude the 2019 if that is indeed the FIRST realization of this on the lattice?

How about somewhat more concise version:

Symmetric mass generation: goes beyond the fermion-bilinear model and introduces non-perturbative interaction effects.(cite 2ish papers verifying this claim) One realization is based on Eichten-Preskill model,(cite) starting from a vector-symmetric fermion model, where chiral fermions and mirror fermions are realized on two domain walls. Gapping the mirror fermion by symmetric mass generation results in chiral fermions at low energy but without fermion doubling.(cite the paper that describes this particular realization. Is that Wang; Wen (2013)? and maybe (2019)) OpenScience709 (talk) 15:09, 17 August 2023 (UTC)

I am following up with the discussion - with OpenScience709: https://en.wikipedia.org/wiki/User_talk:OpenScience709#topics_on_symmetric_mass_generation_removing_fermion-doubling.

>> "goes beyond the fermion-bilinear model and introduces non-perturbative interaction effects"

Ans: arXiv:0904.2197

The effects of interactions on the topological classification of free fermion systems

Lukasz Fidkowski, Alexei Kitaev

However, this work only did gapping 0+1d Marjorana zero modes -- there is no chiral fermion doubling in 0+1d; but only in even spacetime dimensions.

>> "Eichten-Preskill model": I'm happy with including this citation.

Ans: Good idea.

>> As for Wang; Wen (2013). Wang; Wen (2019). Zeng; Zhu; Wang; You (2022): Not all of these are relevant, we only need to include the one that proposed the Eichten-Preskill model spinoff (2013 paper?).

Ans: Wang; Wen (2013; arxiv:1307.7480) has the first lattice model proposed analytically. It was verified only much later numerically by computation simulation in Zeng; Zhu; Wang; You (2022; arxiv:2202.12355)

due to the difficulty of interacting fermion models. Wang; Wen (2019; arxiv:1807.05998) is a variant version of the model published in Physical Review D in lattice field theory.

In this sense, this series of published papers are the first model demonstrating that the Symmetric mass generation works successfully (both analytically and numerically) to give a lattice chiral fermion model.

I would propose to expand other entries' discussions and include a few sentences to explain what those other proposals really mean.

I propose to loop back to the previous edits to include all these references. Meanwhile, some of us and others can expand the discussions on the other approaches: "Ginsparg–Wilson fermion," "Overlap fermion" and "Staggered fermion" and more. 24.187.167.21 (talk) 20:42, 19 August 2023 (UTC)

Three points of clarification:

1. So, to clarify, Lukasz Fidkowski, Alexei Kitaev is the paper that proposed SMG? If so, can we then delete what is currently citations [19-23]?

2. Additionally to clarify: 2013, 2019, 2022 papers are the FIRST papers to show that SMG works in resolving fermion doubling? (the 2013 proposes it, and 2022 demonstrates it explicitly?)

3. The 2019 paper being a variant of the 2013 model does not seem to make it that relevant here however we are only showing how fermion doubling can be overcome in principle and we are not focusing on a comprehensive description of SMG. One example model is sufficient.

So in total we would have 4 citations: arXiv:0904.2197, "Eichten-Preskill model citation, and the 2013, and 2022 papers? OpenScience709 (talk) 16:39, 20 August 2023 (UTC)

Regarding Lukasz Fidkowski, Alexei Kitaev:

(1) There is no concept of the inertial mass in 0+1 spacetime dimension, so it is not quite enough to say the Symmetric Mass Generation is from Lukasz Fidkowski, Alexei Kitaev paper.

The minimal dimension to have a proper concept of the inertial mass requires at least some spatial dimension.

(2) There is no use of the chiral fermion, and the no reference or the idea of the chiral fermion problem in

Lukasz Fidkowski and Alexei Kitaev. So it is probably not enough to only cite Lukasz Fidkowski and Alexei Kitaev.

In my opinion, I would suggest citing based on the appearance on the literature:

(1) Eichten-Preskill model (1986) - which is the precursor, but only discussing gapping the mirror fermion by perturbative calculation.

(2) Lukasz Fidkowski, Alexei Kitaev - arXiv:0904.2197 which is the first on this nonperturbative effect, but only focus on 0+1 dimensions and not yet relevant for chiral fermion problem. They may not be aware the relation of their interactions and the chiral fermion problem.

(3) Wang-Wen (2013; arxiv:1307.7480, PRB), which is the first to propose a well-defined concrete realizable lattice model for chiral fermion for Symmetric Mass Generation on the mirror fermion doubling sector. This model is later verified to work successfully.

(4) David Tong arXiv:2104.03997, which discusses both 1+1 and 3+1 dimensions quantum field theory models, and also discusses chiral fermion problem.

We can also include Razama-Tong "Gapped Chiral Fermions (arXiv:2009.05037) as a pair if we want to have a quantum field theory perspective on SMG gapping the standard model.

(5) Zeng Zhu Wang You (2022; arxiv:2202.12355, PRL), which firstly verifies the Symmetric Mass Generation in 1+1d gapping the mirror chiral fermion on another edge, while leaving the gapless chiral fermion on one edge. This is a nontrivial "numerical or experimental step" to show the SMG gapping mirror fermion is the correct path toward the promised success.

(6) Wang-You (arXiv:2204.14271), which reviews the status of Symmetric Mass Generation (SMG), and gives some various definitions of SMG.

I think all other references on SMG in 2+1 dimensions are less pertinent or irrelevant for lattice chiral fermion doubling, so we can remove them. There are no lattice chiral fermion regularization and fermion doubling problems there. But the above references are somehow the bases to solve the lattice chiral fermion problem in fact in any even spacetime dimensions.

I also think it is not a bad idea to expand the discussions of each entry. And write a few sentences or a paragraph on the meaning of each approach. 2607:FB60:1011:2006:4C58:B4E0:82C8:4E6A (talk) 15:04, 22 August 2023 (UTC)

>> How about somewhat more concise version:

One possibility is this:

Symmetric mass generation [cite David Tong arXiv:2104.03997, Wang-You arXiv:2204.14271]: This approach goes beyond the fermion-bilinear model and introduces non-perturbative interaction effects inspired by Fidkowski-Kitaev [cite arXiv:0904.2197]. One realization is based on Eichten-Preskill model [cite Eichten-Preskill 1986], starting from a vector-symmetric fermion model, where chiral fermions and mirror fermions are realized on two domain walls [can cite Ref.10, Kaplan, D.B.(1992),arXiv:hep-lat/9206013]. Gapping the mirror fermion by symmetric mass generation results in chiral fermions at low energy but without fermion doubling, which has been verified on the lattice analytically and simulated numerically [Wang-Wen arxiv:1307.7480, Zeng-Zhu-Wang-You arxiv:2202.12355].

That seems to perfectly fits all the purpose. 2607:FB60:1011:2006:4C58:B4E0:82C8:4E6A (talk) 15:14, 22 August 2023 (UTC)

>> But the above references are somehow the bases to solve the lattice chiral fermion problem in fact in any even spacetime dimensions.

I believe that here you mean the above references (1)-(6). 2601:184:417F:5919:713E:DB21:547C:897B (talk) 13:32, 23 August 2023 (UTC)

Ok I think we are coming close to an agreement. With some minor rewording and making it a bit more concise:

Symmetric mass generation: This approach goes beyond the fermion-bilinear model and introduces non-perturbative interaction effects.[cite David Tong arXiv:2104.03997, Wang-You arXiv:2204.14271][cite arXiv:0904.2197] One realization based on the Eichten–Preskill model[cite Eichten-Preskill 1986] starts from a vector-symmetric fermion model where chiral fermions and mirror fermions are realized on two domain walls. Gapping the mirror fermion using symmetric mass generation results in chiral fermions at low energy with no fermion doubling.[Wang-Wen arxiv:1307.7480, Zeng-Zhu-Wang-You arxiv:2202.12355]

(I moved the two citations to the end of the first sentence for consistency with how the rest of fermion formulations are cited)

Now we should expand the other fermion realizations in a similar fashion (and similar length of 2-3 sentences), keeping in mind the main point that section should not introduce the fermion formulations themselves. It should instead only elaborate on how they overcome the fermion doubling problem. That's the whole point; this article is about fermion doubling, not about fermions on a lattice.

You said you were willing to do that? I read up on staggered fermions (and wrote its Wiki article), Wilson fermions, and a bit on the Ginsparg-Wilson equation, less so on the others. The fact that I am now a string theorist does help my knowledge :P

It is important that we expand the other fermions sections, otherwise it will given undue emphasis on SMG. OpenScience709 (talk) 20:35, 23 August 2023 (UTC)

Actually, on second though, I'm not sure arXiv:0904.2197 is a relevant citation: you yourself say that it did not exactly establish SMG. So, since we are NOT going into the details of how SMG came about, we don't need to cite it; I presume that David Tong arXiv:2104.03997, Wang-You arXiv:2204.14271 give details validating the "This approach goes beyond the fermion-bilinear model and introduces non-perturbative interaction effects" claim? OpenScience709 (talk) 01:10, 24 August 2023 (UTC)

How about this?

Symmetric mass generation: This approach goes beyond the fermion-bilinear model and introduces non-perturbative interaction effects [cite David Tong arXiv:2104.03997, Wang-You arXiv:2204.14271] generalizing further the four-fermion interactions [cite arXiv:0904.2197]. One realization based on the Eichten–Preskill model [cite Eichten-Preskill 1986] starts from a vector-symmetric fermion model where chiral fermions and mirror fermions are realized on two domain walls. Gapping the mirror fermion using symmetric mass generation results in chiral fermions at low energy with no fermion doubling.[Wang-Wen arxiv:1307.7480, Zeng-Zhu-Wang-You arxiv:2202.12355]

"two domain walls" can cite [Ref.10, Kaplan, D.B.(1992),arXiv:hep-lat/9206013], but it is up to people. 2601:184:417F:5919:1811:DE71:7423:BD36 (talk) 13:08, 24 August 2023 (UTC)

I still don't see how the comment "generalizing further the four-fermion interactions" directly pertains to explaining how SMG overcomes fermion doubling, so still does not seem relevant. It's only providing additional information on the background of SMG itself, something we do not want to go into. All other points are relevant:

• going beyond fermion bilinearity/non-perturbativity are examples of things going against the assumptions of NN, hence are directly relevant.
• The second two sentences are elaborating on how the specific model exactly accomplishes the decoupling between the doublars, so is again relevant.

Kaplan citation is unnecessary since the information is presumably in 1307.7480 anyway. I still advocate for my version without citing arXiv:0904.2197. I'm only being pedantic on this point because the whole idea of this elaboration is that when the reader reads this section, they should be able to directly pick out WHY this mechanism overcomes the Nielsen-Nonomiya theorem. Putting in information about the quartic coupling seems to detract from that point and may leave the reader thinking that "oh maybe its the four-point coupling that causes the theorem to be circumvented", when that's not the fundamental reason. OpenScience709 (talk) 15:23, 24 August 2023 (UTC)

Then, OpenScience709, sure, please go ahead to post your final version! 2601:184:417F:5919:5DC0:4D75:86D:E4A2 (talk) 20:56, 24 August 2023 (UTC)

Done. We should probably start working on expanding the text for the other entries now. OpenScience709 (talk) 09:34, 25 August 2023 (UTC)

I have just read the constructive discussion here.

1. I support the current consensus version.

2. I also do not mean to put "undue emphasis on SMG". My original entry is only one sentence with three citations: "Symmetric mass generation: goes beyond the fermion-bilinear model and introduces non-perturbative interaction effects [cite Wang-Wen arxiv:1307.7480, David Tong arXiv:2104.03997, Zeng-Zhu-Wang-You arxiv:2202.12355]" (03:58, 8 March 2023‎). Anyway, this is no longer a relevant issue for now. Given the current version, I agree that other entries could be expanded.

3. You are right that introducing four-point coupling is not the fundamental reason for SMG to work. The idea of four-point coupling dates long back before SMG and did not work well. The new ingredient in SMG that has been overlooked previously is anomaly cancellation (in particular, discrete global anomalies). The free fermion system may have large emergent symmetry that is anomalous (for example the chiral U(1) symmetry for Weyl fermions prevents gapping because it is anomalous). The interaction must be added in a correct manner to remove these unwanted emergent symmetries (for example the chiral U(1) symmetry is only respected up to its Z4 subgroup in many GUTs), such that the remaining symmetry is anomaly-free and admits a multi-fermion gapping mechanism without breaking the remaining symmetries. The SMG interactions are designed by the guiding principle of anomaly cancellation, which makes it different from previous designs. Everett (talk) 18:41, 14 October 2023 (UTC)