Loops More loops Off-by-one errors Infinite loops Nested Loops.
Braids, loops, and the emergence of the Standard Model · Braids, loops, and the emergence of the...
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Braids, loops, and the emergence of theStandard Model
Sundance Bilson-Thompson
Perimeter Institute, Waterloo ON, Canada
Sundance Bilson-Thompson Braids, loops, and the emergence of the Standard Model
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DISCLAIMER
From Wikipedia
“Dr. Sundance O. Bilson-Thompson is an Australian theoreticalparticle physicist who has developed ideas in the field of loopquantum gravity. He was a Visiting Academic at the Universityof Adelaide before becoming a full-time academic at thePerimeter Institute for Theoretical Physics in Waterloo, Ontario,Canada. He makes terrible puns . Listen for them during hislectures.”
Sundance Bilson-Thompson Braids, loops, and the emergence of the Standard Model
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OUTLINE
1 Basic concepts2 Emergent braided states3 Interpretation as particles4 Systematics of the model
Sundance Bilson-Thompson Braids, loops, and the emergence of the Standard Model
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SHAMELESS HANDWAVING
I will be taking the “mental cartoon” of LQG for granted.Networks of connectionsDual to tetrahedra of space
NB No spin labels necessary at this stage
Consider ribbon networks e.g. as arise in quantum gravitywith non-zero cosmological constant.
Assume ribbon networks are orientable surfaces
Otherwise-arbitrary twisting and braiding allowed
Sundance Bilson-Thompson Braids, loops, and the emergence of the Standard Model
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SHAMELESS HANDWAVING
I will be taking the “mental cartoon” of LQG for granted.Networks of connectionsDual to tetrahedra of space
NB No spin labels necessary at this stage
Consider ribbon networks e.g. as arise in quantum gravitywith non-zero cosmological constant.
Assume ribbon networks are orientable surfaces
Otherwise-arbitrary twisting and braiding allowed
Sundance Bilson-Thompson Braids, loops, and the emergence of the Standard Model
![Page 6: Braids, loops, and the emergence of the Standard Model · Braids, loops, and the emergence of the Standard Model Sundance Bilson-Thompson Perimeter Institute, Waterloo ON, Canada](https://reader033.fdocuments.in/reader033/viewer/2022043015/5f38290a3e76cc53f5774d10/html5/thumbnails/6.jpg)
SHAMELESS HANDWAVING
I will be taking the “mental cartoon” of LQG for granted.Networks of connectionsDual to tetrahedra of space
NB No spin labels necessary at this stage
Consider ribbon networks e.g. as arise in quantum gravitywith non-zero cosmological constant.
Assume ribbon networks are orientable surfaces
Otherwise-arbitrary twisting and braiding allowed
Sundance Bilson-Thompson Braids, loops, and the emergence of the Standard Model
![Page 7: Braids, loops, and the emergence of the Standard Model · Braids, loops, and the emergence of the Standard Model Sundance Bilson-Thompson Perimeter Institute, Waterloo ON, Canada](https://reader033.fdocuments.in/reader033/viewer/2022043015/5f38290a3e76cc53f5774d10/html5/thumbnails/7.jpg)
BRAIDED NETWORKS
If arbitrary braiding is allowed;
Whatever can happen, will
If surfaces are orientable;
Twists into a given node are all even multiples of ±π,and/or zero, or all odd multiples
Sundance Bilson-Thompson Braids, loops, and the emergence of the Standard Model
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A LONG-STANDING QUESTION
If nodes represent volume, and links represent area, whatinformation is encoded by braiding/twisting?
Emergent particle states (says me!)
This possibility can be illustrated by adapting ideas frompreon models
From what?
“Preons? What are they?”
Sundance Bilson-Thompson Braids, loops, and the emergence of the Standard Model
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A LONG-STANDING QUESTION
If nodes represent volume, and links represent area, whatinformation is encoded by braiding/twisting?
Emergent particle states (says me!)
This possibility can be illustrated by adapting ideas frompreon models
From what?
“Preons? What are they?”
Sundance Bilson-Thompson Braids, loops, and the emergence of the Standard Model
![Page 10: Braids, loops, and the emergence of the Standard Model · Braids, loops, and the emergence of the Standard Model Sundance Bilson-Thompson Perimeter Institute, Waterloo ON, Canada](https://reader033.fdocuments.in/reader033/viewer/2022043015/5f38290a3e76cc53f5774d10/html5/thumbnails/10.jpg)
A LONG-STANDING QUESTION
If nodes represent volume, and links represent area, whatinformation is encoded by braiding/twisting?
Emergent particle states (says me!)
This possibility can be illustrated by adapting ideas frompreon models
From what?
“Preons? What are they?”
Sundance Bilson-Thompson Braids, loops, and the emergence of the Standard Model
![Page 11: Braids, loops, and the emergence of the Standard Model · Braids, loops, and the emergence of the Standard Model Sundance Bilson-Thompson Perimeter Institute, Waterloo ON, Canada](https://reader033.fdocuments.in/reader033/viewer/2022043015/5f38290a3e76cc53f5774d10/html5/thumbnails/11.jpg)
A LONG-STANDING QUESTION
If nodes represent volume, and links represent area, whatinformation is encoded by braiding/twisting?
Emergent particle states (says me!)
This possibility can be illustrated by adapting ideas frompreon models
From what?
“Preons? What are they?”
Sundance Bilson-Thompson Braids, loops, and the emergence of the Standard Model
![Page 12: Braids, loops, and the emergence of the Standard Model · Braids, loops, and the emergence of the Standard Model Sundance Bilson-Thompson Perimeter Institute, Waterloo ON, Canada](https://reader033.fdocuments.in/reader033/viewer/2022043015/5f38290a3e76cc53f5774d10/html5/thumbnails/12.jpg)
WHAT PREONS ARE NOT
Preons don’t cause this!!
Sundance Bilson-Thompson Braids, loops, and the emergence of the Standard Model
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RISHONS a.k.a. QUIPS (1979)
Describe all 1st generation quarks and leptons as triplets ofrishons (Harari) or quips (Shupe)
Two types, T and V, plus anti-particles T and V(Harari’s notation)
Ts carry charge +e/3, Ts carry −e/3, Vs and Vs neutral
Assumption: No mixing of anti-rishons and rishons
TTT = e− (TTV,TVT,VTT) = uVVV = νe (TVV,VTV,VVT) = dTTT = e+ (TTV ,TVT ,VTT ) = uVVV = νe (TVV ,VTV ,VVT ) = d
Permutations equivalent to colour charge
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PARTICLE PROPERTIES
Explains number/type of fermions (1st generation)
Explains charge/colour connection
No matter–anti-matter asymmetry
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HELONS - RISHONS WITH A TWIST
Replace Ts and Vs by twisted strands (helons).
Since twists must differ by ±2π, consider H−, H0, and H+.
N.B. Can regard helons as composite = pairs of ±π twists(Tweedles)
Sundance Bilson-Thompson Braids, loops, and the emergence of the Standard Model
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HELONS - RISHONS WITH A TWIST
Replace Ts and Vs by twisted strands (helons).
Since twists must differ by ±2π, consider H−, H0, and H+.
N.B. Can regard helons as composite = pairs of ±π twists(Tweedles)
Sundance Bilson-Thompson Braids, loops, and the emergence of the Standard Model
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HELONS - RISHONS WITH A TWIST
Regard ±2π twists as electric charges ±e/3
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HELONS vs RISHONS
Like rishons in original model, helons are colourless
Like rishons, ordering determines colour
Unlike rishons, we have a reason why ordering matters
Assume triplets with both H+ and H− not allowed
Possible combinations are;
H+H+H+ (e+) H+H+H0 (qu) H+H0H+ (qu) H0H+H+ (qu)H0H0H0 (νe) H0H0H+ (qd) H0H+H0 (qd) H+H0H0 (qd)H−H−H− (e−) H−H−H0 (qu) H−H0H− (qu) H0H−H− (qu)
H0H0H− (qd) H0H−H0 (qd) H−H0H0 (qd)NB: No anti-neutrino
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COMBINING HELONS
Consider braided sub-graphs in isolation (for simplicity)
Remember they are actually attached - even though I don’tdraw them that way!
Sundance Bilson-Thompson Braids, loops, and the emergence of the Standard Model
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FIRST GENERATION FERMIONS
Construct half the 1st generation fermions from +ve andnull twists on a braid
Construct the anti-particles as mirror images
Sundance Bilson-Thompson Braids, loops, and the emergence of the Standard Model
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FIRST GENERATION FERMIONS
Construct half the 1st generation fermions from +ve andnull twists on a braid
Construct the anti-particles as mirror images
Sundance Bilson-Thompson Braids, loops, and the emergence of the Standard Model
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FIRST GENERATION FERMIONS
Construct half the 1st generation fermions from +ve andnull twists on a braid
Construct the anti-particles as mirror images
Sundance Bilson-Thompson Braids, loops, and the emergence of the Standard Model
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CONSERVATION OF BRAIDS
Taking the braid product (joining top-to-bottom) looks a lotlike particle-antiparticle annihilation
Sundance Bilson-Thompson Braids, loops, and the emergence of the Standard Model
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THE MISSING ANTI-NEUTRINOS
Identify left-right mirroring of a braid (or anti-braid) as Pinversion (swapping LH - RH)
Top-bottom mirroring equivalent to C inversion (swappingparticles-antiparticles)
All fermions are essentially neutrinos. Electric charge isjust added to the basic neutrino “framework”
For each non-zero value of electric charge, Q, there arefour combinations of charge and handedness
Q > 0, H =−1 Q > 0, H = +1
Q < 0, H =−1 Q < 0, H = +1
If Q = 0, there are only two possible handedness states -the neutrino and anti-neutrino!
Sundance Bilson-Thompson Braids, loops, and the emergence of the Standard Model
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THE MISSING ANTI-NEUTRINOS
Identify left-right mirroring of a braid (or anti-braid) as Pinversion (swapping LH - RH)
Top-bottom mirroring equivalent to C inversion (swappingparticles-antiparticles)
All fermions are essentially neutrinos. Electric charge isjust added to the basic neutrino “framework”
For each non-zero value of electric charge, Q, there arefour combinations of charge and handedness
Q > 0, H =−1 Q > 0, H = +1
Q < 0, H =−1 Q < 0, H = +1
If Q = 0, there are only two possible handedness states -the neutrino and anti-neutrino!
Sundance Bilson-Thompson Braids, loops, and the emergence of the Standard Model
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THE MISSING ANTI-NEUTRINOS
Identify left-right mirroring of a braid (or anti-braid) as Pinversion (swapping LH - RH)
Top-bottom mirroring equivalent to C inversion (swappingparticles-antiparticles)
All fermions are essentially neutrinos. Electric charge isjust added to the basic neutrino “framework”
For each non-zero value of electric charge, Q, there arefour combinations of charge and handedness
Q > 0, H =−1 Q > 0, H = +1
Q < 0, H =−1 Q < 0, H = +1
If Q = 0, there are only two possible handedness states -the neutrino and anti-neutrino!
Sundance Bilson-Thompson Braids, loops, and the emergence of the Standard Model
![Page 27: Braids, loops, and the emergence of the Standard Model · Braids, loops, and the emergence of the Standard Model Sundance Bilson-Thompson Perimeter Institute, Waterloo ON, Canada](https://reader033.fdocuments.in/reader033/viewer/2022043015/5f38290a3e76cc53f5774d10/html5/thumbnails/27.jpg)
THE MISSING ANTI-NEUTRINOS
Identify left-right mirroring of a braid (or anti-braid) as Pinversion (swapping LH - RH)
Top-bottom mirroring equivalent to C inversion (swappingparticles-antiparticles)
All fermions are essentially neutrinos. Electric charge isjust added to the basic neutrino “framework”
For each non-zero value of electric charge, Q, there arefour combinations of charge and handedness
Q > 0, H =−1 Q > 0, H = +1
Q < 0, H =−1 Q < 0, H = +1
If Q = 0, there are only two possible handedness states -the neutrino and anti-neutrino!
Sundance Bilson-Thompson Braids, loops, and the emergence of the Standard Model
![Page 28: Braids, loops, and the emergence of the Standard Model · Braids, loops, and the emergence of the Standard Model Sundance Bilson-Thompson Perimeter Institute, Waterloo ON, Canada](https://reader033.fdocuments.in/reader033/viewer/2022043015/5f38290a3e76cc53f5774d10/html5/thumbnails/28.jpg)
THE MISSING ANTI-NEUTRINOS
Identify left-right mirroring of a braid (or anti-braid) as Pinversion (swapping LH - RH)
Top-bottom mirroring equivalent to C inversion (swappingparticles-antiparticles)
All fermions are essentially neutrinos. Electric charge isjust added to the basic neutrino “framework”
For each non-zero value of electric charge, Q, there arefour combinations of charge and handedness
Q > 0, H =−1 Q > 0, H = +1
Q < 0, H =−1 Q < 0, H = +1
If Q = 0, there are only two possible handedness states -the neutrino and anti-neutrino!
Sundance Bilson-Thompson Braids, loops, and the emergence of the Standard Model
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HIGHER GENERATIONS
How do we explain 2nd and 3rd generation fermions?
Higher generations = More complex braiding pattern?
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WEAK INTERACTIONS
Link braids top-to-bottom
Twists can spread up and down the strands
Hence charges can be exchanged, turning up quarks intodown quarks, electrons into neutrinos, and so on
Sundance Bilson-Thompson Braids, loops, and the emergence of the Standard Model
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MUON DECAY
Consider muon decay
Topology requires that a νµ be produced
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BOSONS
Weak interactions suggest bosons are braids which inducetrivial permutations
Simplest case;
Formed by joining top-bottom mirror-images.
Other braids which induce trivial permutations arepossible, in principle
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SUMMARY
We can;
Explain existence of all quarks/leptons
Explain why neutrinos are only left-handed
Explain 1:2:3 quark/lepton electric charge ratios
Explain existence of colour charges
Explain why only coloured objects have fractional electriccharge
Describe several generations
Reproduce electroweak interactions
Electric charge (i.e. twist) is quantised. It’s there or it isn’t.
Sundance Bilson-Thompson Braids, loops, and the emergence of the Standard Model
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THE REST OF THE STORY
We also have...
A rule for defining colour interactions
Hypercharge and isospin assignments
We’re working on
Defining different generations precisely
Finding local moves that allow interactions
Identifying/predicting any exotic states
Explaining Cabbibo-mixing/neutrino oscillations
Gracias!
Sundance Bilson-Thompson Braids, loops, and the emergence of the Standard Model
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THE REST OF THE STORY
We also have...
A rule for defining colour interactions
Hypercharge and isospin assignments
We’re working on
Defining different generations precisely
Finding local moves that allow interactions
Identifying/predicting any exotic states
Explaining Cabbibo-mixing/neutrino oscillations
Gracias!
Sundance Bilson-Thompson Braids, loops, and the emergence of the Standard Model
![Page 36: Braids, loops, and the emergence of the Standard Model · Braids, loops, and the emergence of the Standard Model Sundance Bilson-Thompson Perimeter Institute, Waterloo ON, Canada](https://reader033.fdocuments.in/reader033/viewer/2022043015/5f38290a3e76cc53f5774d10/html5/thumbnails/36.jpg)
THE REST OF THE STORY
We also have...
A rule for defining colour interactions
Hypercharge and isospin assignments
We’re working on
Defining different generations precisely
Finding local moves that allow interactions
Identifying/predicting any exotic states
Explaining Cabbibo-mixing/neutrino oscillations
Gracias!
Sundance Bilson-Thompson Braids, loops, and the emergence of the Standard Model
![Page 37: Braids, loops, and the emergence of the Standard Model · Braids, loops, and the emergence of the Standard Model Sundance Bilson-Thompson Perimeter Institute, Waterloo ON, Canada](https://reader033.fdocuments.in/reader033/viewer/2022043015/5f38290a3e76cc53f5774d10/html5/thumbnails/37.jpg)
SWAPPING TWIST FOR BRAIDING
Twists can be turned into braids by flipping nodes over
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NEW MOVES
Braids/twists are invariant under standard local moves.
To allow the interactions of the model, within ribbonnetworks, we need a new move.
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DIRAC SCISSORS AND BELT TRICK
Complex-looking braids, actually trivial!
Related to number of generations? Cabbibo-mixing?
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A QUICK RECAP
The helon model has only a single type of fundamentalobject (tweedles)
There are no assumed charges, spins, or other quantumnumbers
Assumptions:
Orientable surfacesThree types of helons
Tri-valent networksHelons form tripletsBraids automatically have a “top” and “bottom”
No charge mixing (i.e. H+ and H− not allowed together)
Unbraided triplets carry integer charge
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A QUICK RECAP
The helon model has only a single type of fundamentalobject (tweedles)
There are no assumed charges, spins, or other quantumnumbers
Assumptions:
Orientable surfacesThree types of helons
Tri-valent networksHelons form tripletsBraids automatically have a “top” and “bottom”
No charge mixing (i.e. H+ and H− not allowed together)
Unbraided triplets carry integer charge
Sundance Bilson-Thompson Braids, loops, and the emergence of the Standard Model
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THE COLOUR INTERACTION
What happens if we require the same charge on allstrands?
Leptons already fulfill this requirement
Quarks can appear to fulfill this requirement by combining(stacking like pancakes)
Sundance Bilson-Thompson Braids, loops, and the emergence of the Standard Model
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BOSONS - THE GLUONS AND PHOTON
Gluons carrying a colour and an anti-colour arepermutations of +, −, 0
Sundance Bilson-Thompson Braids, loops, and the emergence of the Standard Model