I Fermion doubling problem and three generations of standard model

  • I
  • Thread starter Thread starter kodama
  • Start date Start date
kodama
Messages
1,072
Reaction score
144
TL;DR Summary
origin of three generations
there are three generations of fermions in the standard model with unknown origin

fermion doubling problem that occurs when putting fermions on a spacetime lattice

has there been any research, suggesting that spacetime has a lattice like structure, and that the origin of three generations of fermions in the standard model is in the fermion doubling problem, the three generation copies is in fermion doubling

the fermion doubling problem with some additional work, is the reason there are three generations

the generation construction is that spacetime has a lattice like structure, and putting an electron fermion field on this spacetime results in a fermion doubling, leading to muons and tau fields, and same for quarks.
 
Physics news on Phys.org
kodama said:
the generation construction is that spacetime has a lattice like structure, and putting an electron fermion field on this spacetime results in a fermion doubling, leading to muons and tau fields, and same for quarks.
From https://en.wikipedia.org/wiki/Fermion_doubling:
1754026442151.webp

Can you explain why you think that putting the continuum electron field on a simple 4D lattice could somehow lead to just two additional generations instead of fifteen?
 
renormalize said:
From https://en.wikipedia.org/wiki/Fermion_doubling:
View attachment 363929
Can you explain why you think that putting the continuum electron field on a simple 4D lattice could somehow lead to just two additional generations instead of fifteen?

from the article

Resolutions to fermion doubling​

Therefore, to overcome the fermion doubling problem, one must violate one or more assumptions of the Nielsen–Ninomiya theorem, giving rise to a multitude of proposed resolutions:



These fermion formulations each have their own advantages and disadvantages.<a href="https://en.wikipedia.org/wiki/Fermion_doubling#cite_note-26"><span>[</span>26<span>]</span></a> They differ in the speed at which they can be simulated, the easy of their implementation, and the presence or absence of exceptional configurations. Some of them have a residual chiral symmetry allowing one to simulate axial anomalies. They can also differ in how many of the doublers they eliminate, with some consisting of a doublet, or a quartet of fermions.
https://en.wikipedia.org/wiki/Fermion_doubling



They can also differ in how many of the doublers they eliminate, with some consisting of a doublet, or a quartet of fermions.

if successful eliminate, with some consisting of a doublet, or a quartet of fermions perhaps there's a resolution that gives you 3 generation and only 3 flavors,

either a combination or new theory gives you 3 generation
 
Last edited:
"They can also differ in how many of the doublers they eliminate, with some consisting of a doublet, or a quartet of fermions."
All of the cited known examples of doubling give the number of fermions to be an integer-power of two (0, 2, 4, or 16 total). But if you think you can derive a scheme where the total number due to doubling is odd (namely 3) by all means go ahead and get it published.
 
Last edited:
renormalize said:
"They can also differ in how many of the doublers they eliminate, with some consisting of a doublet, or a quartet of fermions."
All of the cited known examples of doubling give the number of fermions to be an integer-power of two (0, 2, 4, or 16 total). But if you think you can derive a scheme where the total number due to doubling is odd (namely 3) by all means go ahead and get it published.

"All of the cited known examples of doubling give the number of fermions to be an integer-power of two (0, 2, 4, or 16 total)."

perhaps instead a simple 4D lattice, try a 3D spatial lattice to get odd
 
kodama said:
perhaps instead a simple 4D lattice, try a 3D spatial lattice to get odd
But Wikipedia says:
1754081069892.webp

That suggests to me that a 3D lattice could give rise to 1, 2, 4, or 8 generations, not an odd number like 3. But that's just my guess. Did you research "fermion doubling" before posting here on PF? Or are you just spitballing ideas without first checking the literature?
 
kodama said:
has there been any research
The fact that you are asking this question indicates that you don't have any references to back up this:

kodama said:
the fermion doubling problem with some additional work, is the reason there are three generations

the generation construction is that spacetime has a lattice like structure, and putting an electron fermion field on this spacetime results in a fermion doubling, leading to muons and tau fields, and same for quarks.
Without a valid references as a basis for discussion, we can't discuss this since it's just your personal speculation, which is off limits here. Do you have a reference?
 
Reply
  • Like
Likes renormalize and weirdoguy
PeterDonis said:
The fact that you are asking this question indicates that you don't have any references to back up this:


Without a valid references as a basis for discussion, we can't discuss this since it's just your personal speculation, which is off limits here. Do you have a reference?
Gupta, R. (1997). "Introduction to lattice QCD: Course". Les Houches Summer School in Theoretical Physics, Session 68: Probing the Standard Model of Particle Interactions: 83–219. arXiv:hep-lat/9807028.

Follana, E.; et al. (HPQCD,UKQCD) (2007). "Highly Improved Staggered Quarks on the Lattice, with Applications to Charm Physics". Phys. Rev. D. 75 (5): 054502. arXiv:hep-lat/0610092.

DeGrand, T.; DeTar, C. (2006). "6". Lattice Methods for Quantum Chromodynamics. World Scientific Publishing. p. 103. Bibcode:2006lmqc.book.....D. doi:10.1142/6065. ISBN 978-9812567277.

Gattringer, C.; Lang, C.B. (2009). "5". Quantum Chromodynamics on the Lattice: An Introductory Presentation. Lecture Notes in Physics 788. Springer. pp. 111–112. doi:10.1007/978-3-642-01850-3. ISBN 978-3642018497.

Rothe, H.J. (2005). "3". Lattice Gauge Theories: An Introduction. World Scientific Lecture Notes in Physics: Volume 43. Vol. 82. World Scientific Publishing. pp. 39–40. doi:10.1142/8229. hdl:20.500.12657/50492. ISBN 978-9814365857.
 
kodama said:
that quotations is from renormalize
That is simply not true. Here is your original post containing the statements quoted by @PeterDonis:
kodama said:
TL;DR Summary: origin of three generations

there are three generations of fermions in the standard model with unknown origin

fermion doubling problem that occurs when putting fermions on a spacetime lattice

has there been any research, suggesting that spacetime has a lattice like structure, and that the origin of three generations of fermions in the standard model is in the fermion doubling problem, the three generation copies is in fermion doubling

the fermion doubling problem with some additional work, is the reason there are three generations

the generation construction is that spacetime has a lattice like structure, and putting an electron fermion field on this spacetime results in a fermion doubling, leading to muons and tau fields, and same for quarks.
 
  • #10
kodama said:
Gupta, R. (1997). "Introduction to lattice QCD: Course". Les Houches Summer School in Theoretical Physics, Session 68: Probing the Standard Model of Particle Interactions: 83–219. arXiv:hep-lat/9807028.

Follana, E.; et al. (HPQCD,UKQCD) (2007). "Highly Improved Staggered Quarks on the Lattice, with Applications to Charm Physics". Phys. Rev. D. 75 (5): 054502. arXiv:hep-lat/0610092.

DeGrand, T.; DeTar, C. (2006). "6". Lattice Methods for Quantum Chromodynamics. World Scientific Publishing. p. 103. Bibcode:2006lmqc.book.....D. doi:10.1142/6065. ISBN 978-9812567277.

Gattringer, C.; Lang, C.B. (2009). "5". Quantum Chromodynamics on the Lattice: An Introductory Presentation. Lecture Notes in Physics 788. Springer. pp. 111–112. doi:10.1007/978-3-642-01850-3. ISBN 978-3642018497.

Rothe, H.J. (2005). "3". Lattice Gauge Theories: An Introduction. World Scientific Lecture Notes in Physics: Volume 43. Vol. 82. World Scientific Publishing. pp. 39–40. doi:10.1142/8229. hdl:20.500.12657/50492. ISBN 978-9814365857.
These are all nice general references about lattice QCD. Where, specifically, do they make the claims you made that I quoted?
 
  • #11
PeterDonis said:
These are all nice general references about lattice QCD. Where, specifically, do they make the claims you made that I quoted?
I was asking a question
 
  • #12
kodama said:
I was asking a question
What I quoted from your OP were statements, not questions. Here, I'll quote the same again:

kodama said:
the fermion doubling problem with some additional work, is the reason there are three generations

the generation construction is that spacetime has a lattice like structure, and putting an electron fermion field on this spacetime results in a fermion doubling, leading to muons and tau fields, and same for quarks.
No questions there. If you think the references you gave justify these statements, please say specifically where.
 
Reply
  • Like
Likes Motore and weirdoguy
  • #13
Fermion doubling is just one form of a broader phenomenon, in which de facto extra fermions are brought about by the existence of extra zero-energy modes or "zero modes" of a fermionic field. A version of this actually occurs in string theory - the number of generations produced by a Calabi-Yau depends on how many independent "harmonic forms" are allowed by the Calabi-Yau. In all cases, the idea is that you have a fermionic field which by itself in a flat space would just count as one fermion, but because of extra structure like latticization or complicated spatial topology, there are extra zero-energy vibratory modes which are independent of each other, and thus count de facto as distinct fermion species.

Fermion doubling occurs because one is dealing with periodic waveforms that necessarily cross the "x=0" axis of energy in pairs (just like the hill-and-valley structure of sine and cosine waves), so the zero modes also come in pairs. Like @renormalize said, lattices naturally produce powers-of-two doubling. In fact, since there are 16 fermionic states in a standard model generation (if you include right-handed neutrinos), it has been suggested that fermion doubling (in the four directions of space-time, thus 2^4 = 16) is responsible, not for the number of generations, but for the number of fermions in a single generation!

To explain the number of generations using extra zero modes, either you need something to make fourth-and-higher generations extra heavy, or you need a zero-mode mechanism which is not doubling per se.

Papers along all these lines exist (e.g. Kaplan-Sun, Bentov-Zee) but I have not studied them to see how plausible they are.

In addition, if one is talking about zero modes created by latticization or discretization of space-time, one should recall that breaking up the space-time continuum in this way creates other problems, like a breakdown in rotational symmetry of space-time that should affect conservation of angular momentum. Recovering the continuum limit of space-time is one of loop quantum gravity's greatest problems!

By the way, digressing for a moment on the topic of the Ashtekar variables that loop quantum gravity employs, I have proposed for some time that the variables are valid but that LQG quantizes them "wrongly" (i.e. in a way that doesn't describe reality), and that there is probably a way to quantize them which outputs the usual effective theory of quantum gravity (that's normally described in terms of gravitons)... Maybe that's true, but the loop basis that LQG uses (and which is the origin of its version of discretized space-time) is pretty natural, so an important question would be, how does this other way to quantize the Ashtekar variables (which is hinted at, in at least two papers) look from the perspective of the loop basis? That might give us an inkling of the right way to think about "quantization of space-time".
 
Reply
  • Like
Likes kodama and renormalize
  • #14
PeterDonis said:
What I quoted from your OP were statements, not questions. Here, I'll quote the same again:


No questions there. If you think the references you gave justify these statements, please say specifically where.

you omitted

has there been any research, suggesting that spacetime has a lattice like structure, and that the origin of three generations of fermions in the standard model is in the fermion doubling problem, the three generation copies is in fermion doubling

that is a question
 
  • #15
mitchell porter said:
By the way, digressing for a moment on the topic of the Ashtekar variables that loop quantum gravity employs, I have proposed for some time that the variables are valid but that LQG quantizes them "wrongly" (i.e. in a way that doesn't describe reality), and that there is probably a way to quantize them which outputs the usual effective theory of quantum gravity (that's normally described in terms of gravitons)... Maybe that's true, but the loop basis that LQG uses (and which is the origin of its version of discretized space-time) is pretty natural, so an important question would be, how does this other way to quantize the Ashtekar variables (which is hinted at, in at least two papers) look from the perspective of the loop basis? That might give us an inkling of the right way to think about "quantization of space-time".

could you elaborate on this other way to quantize the Ashtekar variables hat might give us an inkling of the right way to think about "quantization of space-time?
 
  • #16
kodama said:
could you elaborate on this other way to quantize the Ashtekar variables hat might give us an inkling of the right way to think about "quantization of space-time?
I can first name the two papers that I mentioned:

"Path integral for the Hilbert-Palatini and Ashtekar gravity" (Alexandrov and Vassilevich 1998)

"Generalized Symmetry in Dynamical Gravity" (Clifford Cheung et al 2024)

Also see the last paragraph of this comment from last year.

The 1998 paper is directly a quantization of general relativity in Ashtekar variables, but not using LQG methods. I believe it should be equivalent to the usual perturbative quantization that leads to gravitons, but that needs to be checked. The 2024 paper is something similar and even (page 26) derives an expression very similar to the LQG area operator. So this is a place where the comparison with LQG could potentially be very sophisticated. We have a theoretical framework which is basically perturbative quantum gravity with a change of variables, and yet we have some area-like quantity similar to LQG. It's an opportunity to drill into the details of what makes these two approaches to quantum gravity different, and what the consequences are.
 
  • #17
kodama said:
you omitted

has there been any research, suggesting that spacetime has a lattice like structure, and that the origin of three generations of fermions in the standard model is in the fermion doubling problem, the three generation copies is in fermion doubling

that is a question
Yes, I know, but your claims later on in the same post, which I quoted, are claimed answers to that question. That makes it seem like you're not really asking the question, you're pushing your preferred answer.
 
  • #18
mitchell porter said:
Fermion doubling is just one form of a broader phenomenon, in which de facto extra fermions are brought about by the existence of extra zero-energy modes or "zero modes" of a fermionic field. A version of this actually occurs in string theory - the number of generations produced by a Calabi-Yau depends on how many independent "harmonic forms" are allowed by the Calabi-Yau. In all cases, the idea is that you have a fermionic field which by itself in a flat space would just count as one fermion, but because of extra structure like latticization or complicated spatial topology, there are extra zero-energy vibratory modes which are independent of each other, and thus count de facto as distinct fermion species.

Fermion doubling occurs because one is dealing with periodic waveforms that necessarily cross the "x=0" axis of energy in pairs (just like the hill-and-valley structure of sine and cosine waves), so the zero modes also come in pairs. Like @renormalize said, lattices naturally produce powers-of-two doubling.

could you either change the dimensions of the lattices, or change the nature and properties of the lattice, such as spin networks, or use a topology in 4d space-time to get powers of 3

A Lattice Physics Approach to Spin-Networks in Loop Quantum Gravity
Noah M. MacKay
 
  • #19
kodama said:
that is a question

So maybe you should use a question mark?
 

Similar threads

A Furey's superalgebra and the standard model
Replies
4
Views
1K
A Three generations of Fermions from octonions Clifford alegbras
2
Replies
61
Views
8K
I Lattice standard model (Wang & Wen)
Replies
1
Views
2K
I The standard model from loop quantum gravity via spinors octonions
Replies
26
Views
4K
A Reviving Kaluza-Klein: SM Bosons & Fermions
Replies
4
Views
2K
I All possible models to explain the hierarchy problem?
Replies
0
Views
2K
A Seeking the Standard Model in E8 plus Supersymmetry
Replies
4
Views
3K
A The Exceptional Jordan Algebra in physics
Replies
3
Views
3K
I Supersymmetry breaking and hidden sector
Replies
3
Views
2K
A "Monstrous Higgs and Leech Spacetime"
Replies
0
Views
3K

Hot Threads

Recent Insights

Back
Top