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Hilbert Space
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Related Publications
(17)
Locality and translations in braided ribbon networks
On Braid Excitations in Quantum Gravity
Propagation and interaction of chiral states in quantum gravity
Conserved quantities for interacting 4valent braids in quantum gravity
Particle Identifications from Symmetries of Braided Ribbon Network Invariants
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Quantum gravity and the standard model
Quantum gravity and the standard model,10.1088/02649381/24/16/002,Classical and Quantum Gravity,Sundance O. BilsonThompson,Fotini Markopoulou,Lee Sm
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Quantum gravity and the standard model
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Citations: 38
)
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Sundance O. BilsonThompson
,
Fotini Markopoulou
,
Lee Smolin
We show that a class of backgroundindependent models of quantum spacetime have local excitations that can be mapped to the firstgeneration fermions of the
standard model
of particle physics. These states propagate coherently as they can be shown to be noiseless subsystems of the microscopic
quantum dynamics
(Kribs and Markopoulou 2005 Preprint grqc/0510052, Markopoulou and Poulin unpublished). These are identified in terms of certain patterns of braiding of graphs, thus giving a quantum gravitational foundation for the topological preon model proposed by BilsonThompson (2005 Preprint hepph/0503213). These results apply to a large class of theories in which the
Hilbert space
has a basis of states given by ribbon graphs embedded in a threedimensional manifold up to diffeomorphisms, and the dynamics is given by local moves on the graphs, such as arise in the
representation theory
of quantum groups. For such models, matter appears to be already included in the microscopic kinematics and dynamics.
Journal:
Classical and Quantum Gravity  CLASS QUANTUM GRAVITY
, vol. 24, no. 16, pp. 39753993, 2007
DOI:
10.1088/02649381/24/16/002
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Citation Context
(19)
...There has been a large amount of research effort towards a quantum theory of gravity with matter as topological invariants since a ribbonized preon model[1] was coded into local braided ribbon excitations[
2
]...
...The results of [
2
] have a serious limitation, namely that the conservation laws which preserve the excitations are exact...
...In other words, the braid excitations of [
2
] behave like solitons in integrable systems: they propagate through each other under local dynamical moves, leaving no possibility for interaction, e.g...
...Consequently, interpreting braid excitations found in [
2
] as particles  in particular the Standard Model particles  is not going to work out unless interactions are successfully introduced to that model...
...Although there has been a search for a modification of the dynamics studied in [
2
] which would allow both propagation and interactions of the local braid excitations, a new model has also been put forward, which solves the problem of interaction and opens new interesting directions worth of investigation[5, 6]...
...Indeed, as a followup work of [
2
], in [8] similar algebraic approach is being taken for threevalent spin networks, in which each ribbon braid is only characterized by three integers: the socalled Louis numbers, named after Louis Kauffman...
...Fig. 7 shows two activelyinteracting trivial braids[6], algebraically they areB1 = + 1 [1; 1; 1] + andB2 = + [T + 2; 0; 0] + . One sees that B1 +B2 = + 1 [1; 1; 1] + + + 2 [
2
; 0; 0] +...
...= + 1 [1; 1; 1] + #R2; 2( + 2 [
2
; 0; 0] + )...
...2 = + 1 [1; 1; 1] + # + 0 [0; 0;
2
] + 2 = + 1 [1; 1; 1] + 2 :...
...On the other hand, B1 +B2 = + 1 [1; 1; 1] + + + 2 [
2
; 0; 0] +...
...= R 2;2( + 1 [1; 1; 1] + 2 ) # + 0 [
2
; 0; 0] +...
...= R 2;2( + 1 [1; 1; 1] + 2 ) # + 0 [2; 0; 0] + = + 3 [ 1; 1; 1] + # + 0 [
2
; 0; 0] +...
Jonathan Hackett
,
et al.
Conserved quantities for interacting 4valent braids in quantum gravit...
...A substantial amount of work[
1
, 2, 3, 4, 5, 6, 7, 8, 9] has been done recently towards emergent matter as topological invariants of framed spin networks, embedded in a topological threemanifold[1, 2, 3, 4, 5, 6, 7, 8] and unembedded[9], as fundamental states of quantum gravity and quantum geometry...
...A substantial amount of work[1, 2, 3, 4, 5, 6, 7, 8, 9] has been done recently towards emergent matter as topological invariants of framed spin networks, embedded in a topological threemanifold[
1
, 2, 3, 4, 5, 6, 7, 8] and unembedded[9], as fundamental states of quantum gravity and quantum geometry...
...Some papers study the case of framed threevalent spin networks[
1
, 2, 3, 9], which were motivated by the pioneer work of BilsonThompson [10]...
...The aim of this paper is to present an effective description of these emergent local excitations[
1
, 5, 11] in the language of Feynman diagrams...
...The threevalent case considered in [
1
, 2, 3] is limited by la ck of creation and annihilation of the topological invariants[2] which are considered corresponding to Standard Model particles[3]...
Yidun Wan
.
Effective theory of braid excitations of quantum geometry in terms of ...
...Recent work [1,
2
] suggests that topological features of certain quantum gravity theories can be interpreted as particles, matching the known fermions and bosons of the rst generation in the Standard Model...
...This idea was soon adapted to interpret extra topological degrees of freedom occurring in certain theories of quantum gravity [
2
], raising the exciting possibility that matter may be an emergent feature of quantum gravity theories...
...On the left of Fig. 3 we illustrate a Yshaped ribbon  that is, a node with three ribbons or \legs" attached to it. Such a triple of ribbons meeting at a node has previously been referred to as a \trinion" [
2
], and we shall adopt this terminology...
...In [
2
] it was shown that braided belts attached at one end to a larger network of ribbons could be used to represent the elementary quarks and leptons...
...In order to keep the discussion in this paper relevant to the work in [
2
], we shall henceforth treat the ordering of generators in a braid word as indicative of a \top end" which is free to be trinionipped, and a \bottom end" which is attached to a larger network (which for all practical purposes is xed and static)...
...The resulting pure twistword is found to be [1;
2
; 1]...
...Thus [
2
; 0; 1] gives the framings on the equivalent parallel at strip belt...
Sundance BilsonThompson
,
et al.
Particle topology, braids, and braided belts
...Recently it was discovered that this is realized in the context of models of quantum geometry based on spin networks, such as those used in loop quantum gravity and spin foam models[1, 2,
3
]. Although the rough idea that topological features of spacetime qeometry might be interpreted as particles is very old, two questions delayed implementation of the idea till recently...
...In [
3
] it was shown that this was the case in a simple model of the dynamics of quantum geometry...
...Strikingly, the results of [
3
] make contact with both structures from topological quantum computing and now classic results of knot theory from the 1980s...
...However, the results of [
3
] suffered from a serious limitation...
...Indeed, as shown by [7] the braided excitations of [
3
] are like solitons in integrable systems: they pass right through each other...
...This means that interactions necessary to turn the game coded in [
3
] into a real theory of the standard model do not appear to exist in that model...
...As a result, a search has been underway for a modification of the dynamics studied in [
3
] which would allow propagation and interactions of emergent chiral matter degrees of freedom[8]...
...This is not so easy as many extensions of the local moves studied in [
3
] destabalize the braids so that there are no longer any emergent conservation laws...
...We do not however, in this paper, investigate the correspondence to the preon models of [4,
3
]...
Lee Smolin
,
et al.
Propagation and interaction of chiral states in quantum gravity
...(It could, however, be possible that additional degrees of freedom emerge in a yet to be developed effective description; see, e.g., [
18
]f or a suggestion.) What is realized in loop quantum gravity and in fact presents one of its main features is an underlying discrete structure of space [10,11,62], so that one may at least address the first part of the problem...
Martin Bojowald
.
The dark side of a patchwork universe
References
(2)
Knots and Physics
(
Citations: 331
)
Louis Kauffman
,
Aiyalam P. Balachandran
Journal:
Physics Today  PHYS TODAY
, vol. 45, no. 4, 1992
Notes on Physics
(
Citations: 98
)
Unknown
Journal:
Science
, vol. 8, no. 195, pp. 403405, 1898
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Citations
(38)
Particle creation from vacuum by Lorentz violation
Nima Khosravi
Journal:
General Relativity and Gravitation  GEN RELATIV GRAVIT
, vol. 43, no. 5, pp. 14171426, 2011
Loop quantum gravity: the first twenty five years
(
Citations: 1
)
Carlo Rovelli
Published in 2010.
On the geometrization of matter by exotic smoothness
Torsten AsselmeyerMaluga
,
Helge Rose
Published in 2010.
AP Theory III: Conelike Graded SUSY, Dynamic Dark Energy and the YM Millenium Problem
H. E. Winkelnkemper
Published in 2010.
Embedding the BilsonThompson model in an LQGlike framework
Deepak Vaid
Published in 2010.