• Braids, loops, and the emergence of the Standard Model


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  • FileName: Bilson-Thompson.pdf [read-online]
    • Abstract: Braids, loops, and the emergence of the Standard Model. SHAMELESS HANDWAVING. I will be taking the "mental cartoon" of LQG for granted. Networks of connections. Dual to tetrahedra of space. NB No spin labels necessary at this stage. Consider ribbon n

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Braids, loops, and the emergence of the
Standard Model
Sundance Bilson-Thompson
Perimeter Institute, Waterloo ON, Canada
Sundance Bilson-Thompson Braids, loops, and the emergence of the Standard Model
DISCLAIMER
From Wikipedia
“Dr. Sundance O. Bilson-Thompson is an Australian theoretical
particle physicist who has developed ideas in the field of loop
quantum gravity. He was a Visiting Academic at the University
of Adelaide before becoming a full-time academic at the
Perimeter Institute for Theoretical Physics in Waterloo, Ontario,
Canada. He makes terrible puns. Listen for them during his
lectures.”
Sundance Bilson-Thompson Braids, loops, and the emergence of the Standard Model
OUTLINE
1 Basic concepts
2 Emergent braided states
3 Interpretation as particles
4 Systematics of the model
Sundance Bilson-Thompson Braids, loops, and the emergence of the Standard Model
SHAMELESS HANDWAVING
I will be taking the “mental cartoon” of LQG for granted.
Networks of connections
Dual to tetrahedra of space
NB No spin labels necessary at this stage
Consider ribbon networks e.g. as arise in quantum gravity
with 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
SHAMELESS HANDWAVING
I will be taking the “mental cartoon” of LQG for granted.
Networks of connections
Dual to tetrahedra of space
NB No spin labels necessary at this stage
Consider ribbon networks e.g. as arise in quantum gravity
with 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
SHAMELESS HANDWAVING
I will be taking the “mental cartoon” of LQG for granted.
Networks of connections
Dual to tetrahedra of space
NB No spin labels necessary at this stage
Consider ribbon networks e.g. as arise in quantum gravity
with 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
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
A LONG-STANDING QUESTION
If nodes represent volume, and links represent area, what
information is encoded by braiding/twisting?
Emergent particle states (says me!)
This possibility can be illustrated by adapting ideas from
preon models
From what?
“Preons? What are they?”
Sundance Bilson-Thompson Braids, loops, and the emergence of the Standard Model
A LONG-STANDING QUESTION
If nodes represent volume, and links represent area, what
information is encoded by braiding/twisting?
Emergent particle states (says me!)
This possibility can be illustrated by adapting ideas from
preon models
From what?
“Preons? What are they?”
Sundance Bilson-Thompson Braids, loops, and the emergence of the Standard Model
A LONG-STANDING QUESTION
If nodes represent volume, and links represent area, what
information is encoded by braiding/twisting?
Emergent particle states (says me!)
This possibility can be illustrated by adapting ideas from
preon models
From what?
“Preons? What are they?”
Sundance Bilson-Thompson Braids, loops, and the emergence of the Standard Model
A LONG-STANDING QUESTION
If nodes represent volume, and links represent area, what
information is encoded by braiding/twisting?
Emergent particle states (says me!)
This possibility can be illustrated by adapting ideas from
preon models
From what?
“Preons? What are they?”
Sundance Bilson-Thompson Braids, loops, and the emergence of the Standard Model
WHAT PREONS ARE NOT
Preons don’t cause this!!
Sundance Bilson-Thompson Braids, loops, and the emergence of the Standard Model
RISHONS a.k.a. QUIPS (1979)
Describe all 1st generation quarks and leptons as triplets of
rishons (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) = u
VVV = νe (TVV, VTV, VVT) = d
TTT = e+ (TTV, TVT, VTT) = u
VVV = νe (TVV, VTV, VVT) = d
Permutations equivalent to colour charge
Sundance Bilson-Thompson Braids, loops, and the emergence of the Standard Model
PARTICLE PROPERTIES
Explains number/type of fermions (1st generation)
Explains charge/colour connection
No matter–anti-matter asymmetry
Sundance Bilson-Thompson Braids, loops, and the emergence of the Standard Model
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
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
HELONS - RISHONS WITH A TWIST
Regard ±2π twists as electric charges ±e/3
Sundance Bilson-Thompson Braids, loops, and the emergence of the Standard Model
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+ H0 H+ (qu ) H0 H+ H+ (qu )
H0 H0 H0 (νe ) H0 H0 H+ (qd ) H0 H+ H0 (qd ) H+ H0 H0 (qd )
H− H− H− (e− ) H− H− H0 (qu ) H− H0 H− (qu ) H0 H− H− (qu )
H0 H0 H− (qd ) H0 H− H0 (qd ) H− H0 H0 (qd )
NB: No anti-neutrino
Sundance Bilson-Thompson Braids, loops, and the emergence of the Standard Model
COMBINING HELONS
Consider braided sub-graphs in isolation (for simplicity)
Remember they are actually attached - even though I don’t
draw them that way!
Sundance Bilson-Thompson Braids, loops, and the emergence of the Standard Model
FIRST GENERATION FERMIONS
Construct half the 1st generation fermions from +ve and
null twists on a braid
Sundance Bilson-Thompson Braids, loops, and the emergence of the Standard Model
FIRST GENERATION FERMIONS
Construct half the 1st generation fermions from +ve and
null twists on a braid
Construct the anti-particles as mirror images
Sundance Bilson-Thompson Braids, loops, and the emergence of the Standard Model
FIRST GENERATION FERMIONS
Construct half the 1st generation fermions from +ve and
null twists on a braid
Construct the anti-particles as mirror images
Sundance Bilson-Thompson Braids, loops, and the emergence of the Standard Model
CONSERVATION OF BRAIDS
Taking the braid product (joining top-to-bottom) looks a lot
like particle-antiparticle annihilation
Sundance Bilson-Thompson Braids, loops, and the emergence of the Standard Model
THE MISSING ANTI-NEUTRINOS
Identify left-right mirroring of a braid (or anti-braid) as P
inversion (swapping LH - RH)
Top-bottom mirroring equivalent to C inversion (swapping
particles-antiparticles)
All fermions are essentially neutrinos. Electric charge is
just added to the basic neutrino “framework”
For each non-zero value of electric charge, Q, there are
four 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
THE MISSING ANTI-NEUTRINOS
Identify left-right mirroring of a braid (or anti-braid) as P
inversion (swapping LH - RH)
Top-bottom mirroring equivalent to C inversion (swapping
particles-antiparticles)
All fermions are essentially neutrinos. Electric charge is
just added to the basic neutrino “framework”
For each non-zero value of electric charge, Q, there are
four 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
THE MISSING ANTI-NEUTRINOS
Identify left-right mirroring of a braid (or anti-braid) as P
inversion (swapping LH - RH)
Top-bottom mirroring equivalent to C inversion (swapping
particles-antiparticles)
All fermions are essentially neutrinos. Electric charge is
just added to the basic neutrino “framework”
For each non-zero value of electric charge, Q, there are
four 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
THE MISSING ANTI-NEUTRINOS
Identify left-right mirroring of a braid (or anti-braid) as P
inversion (swapping LH - RH)
Top-bottom mirroring equivalent to C inversion (swapping
particles-antiparticles)
All fermions are essentially neutrinos. Electric charge is
just added to the basic neutrino “framework”
For each non-zero value of electric charge, Q, there are
four 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
THE MISSING ANTI-NEUTRINOS
Identify left-right mirroring of a braid (or anti-braid) as P
inversion (swapping LH - RH)
Top-bottom mirroring equivalent to C inversion (swapping
particles-antiparticles)
All fermions are essentially neutrinos. Electric charge is
just added to the basic neutrino “framework”
For each non-zero value of electric charge, Q, there are
four 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
HIGHER GENERATIONS
How do we explain 2nd and 3rd generation fermions?
Higher generations = More complex braiding pattern?
Sundance Bilson-Thompson Braids, loops, and the emergence of the Standard Model
WEAK INTERACTIONS
Link braids top-to-bottom
Twists can spread up and down the strands
Hence charges can be exchanged, turning up quarks into
down quarks, electrons into neutrinos, and so on
Sundance Bilson-Thompson Braids, loops, and the emergence of the Standard Model
MUON DECAY
Consider muon decay
Topology requires that a νµ be produced
Sundance Bilson-Thompson Braids, loops, and the emergence of the Standard Model
BOSONS
Weak interactions suggest bosons are braids which induce
trivial permutations
Simplest case;
Formed by joining top-bottom mirror-images.
Other braids which induce trivial permutations are
possible, in principle
Sundance Bilson-Thompson Braids, loops, and the emergence of the Standard Model
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 electric
charge
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
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
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
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
SWAPPING TWIST FOR BRAIDING
Twists can be turned into braids by flipping nodes over
Sundance Bilson-Thompson Braids, loops, and the emergence of the Standard Model
NEW MOVES
Braids/twists are invariant under standard local moves.
To allow the interactions of the model, within ribbon
networks, we need a new move.
Sundance Bilson-Thompson Braids, loops, and the emergence of the Standard Model
DIRAC SCISSORS AND BELT TRICK
Complex-looking braids, actually trivial!
Related to number of generations? Cabbibo-mixing?
Sundance Bilson-Thompson Braids, loops, and the emergence of the Standard Model
A QUICK RECAP
The helon model has only a single type of fundamental
object (tweedles)
There are no assumed charges, spins, or other quantum
numbers
Assumptions:
Orientable surfaces
Three types of helons
Tri-valent networks
Helons form triplets
Braids 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
A QUICK RECAP
The helon model has only a single type of fundamental
object (tweedles)
There are no assumed charges, spins, or other quantum
numbers
Assumptions:
Orientable surfaces
Three types of helons
Tri-valent networks
Helons form triplets
Braids 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
THE COLOUR INTERACTION
What happens if we require the same charge on all
strands?
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
BOSONS - THE GLUONS AND PHOTON
Gluons carrying a colour and an anti-colour are
permutations of +, −, 0
Sundance Bilson-Thompson Braids, loops, and the emergence of the Standard Model


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