Origin of Symmetries

Froggatt, C.D.; Nielsen, Holger Bech

doi:10.1142/0090

Cited by 168 publications

(193 citation statements)

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“…the approach that tries to view either special or general theory of relativity not as primitive concepts but rather as theories that statistically emerge from a deeper (essentially non-relativistic) level of dynamics [16,19,[36][37][38][39][40][41].…”

Section: Emergent Special Relativitymentioning

confidence: 99%

Emergence of special and doubly special relativity

Jizba

Scardigli

2012

Phys. Rev. D

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Building on our previous work [Phys. Rev. D82, 085016 (2010)], we show in this paper how a Brownian motion on a short scale can originate a relativistic motion on scales that are larger than particle's Compton wavelength. This can be described in terms of polycrystalline vacuum. Viewed in this way, special relativity is not a primitive concept, but rather it statistically emerges when a coarse graining average over distances of order, or longer than the Compton wavelength is taken. By analyzing the robustness of such a special relativity under small variations in the polycrystalline grain-size distribution we naturally arrive at the notion of doubly-special relativistic dynamics. In this way, a previously unsuspected, common statistical origin of the two frameworks is brought to light. Salient issues such as the rôle of gauge fixing in emergent relativity, generalized commutation relations, Hausdorff dimensions of representative path-integral trajectories and a connection with Feynman chessboard model are also discussed.

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Section: Emergent Special Relativitymentioning

confidence: 99%

Emergence of special and doubly special relativity

Jizba

Scardigli

2012

Phys. Rev. D

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“…The point nodes in the spectrum of chiral quarks and leptons are topologically protected as well as their condensed matter counterparts, which are called Dirac or Weyl points (on the topology of Weyl points in particle physics and condensed matter see, e.g., Refs. [1][2][3][4][5].…”

Section: Introductionmentioning

confidence: 99%

Topological Fermi arcs in superfluid3He

Силаев

Volovik

2012

Phys. Rev. B

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We consider fermionic states bound on domain walls in a Weyl superfluid 3 He-A and on interfaces between 3 He-A and a fully gapped topological superfluid 3 He-B. We demonstrate that in both cases the fermionic spectrum contains Fermi arcs that are continuous nodal lines of energy spectrum terminating at the projections of two Weyl points to the plane of surface states in momentum space. The number of Fermi arcs is determined by the index theorem that relates bulk values of the topological invariant to the number of zero-energy surface states. The index theorem is consistent with an exact spectrum of Bogolubov-de Gennes equation obtained numerically, meanwhile, the quasiclassical approximation fails to reproduce the correct number of zero modes. Thus we demonstrate that topology describes the properties of the exact spectrum beyond the quasiclassical approximation.

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“…The observed hierarchy of charged fermion masses and quark mixing angles strongly suggests the existence of an approximate chiral flavour symmetry [1] beyond the standard model (SM). In a previous paper [2] we discussed the implications of such a symmetry for neutrino masses and mixings.…”

Section: Introductionmentioning

confidence: 99%

Neutrino masses and mixings from an anomaly free SMG×U(1)2 model

Froggatt

Gibson

Nielsen³

1999

Physics Letters B

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A natural solution to the fermion mass hierarchy problem suggests the existence of a partially conserved chiral symmetry. We show that this can lead to a reasonably natural solution to the solar and atmospheric neutrino problems without fine-tuning or the addition of new low energy fermions. The atmospheric neutrino atmospheric neutrino anomaly is given by large mixing between ν µ and ν τ , with ∆m 2 atm ∼ 10 −3 eV 2 , and the solar neutrino deficit is due to nearly maximal electron neutrino vacuum oscillations. We present an explicit model for the neutrino masses which is an anomaly free Abelian extension of the standard model that also yields a realistic charged fermion spectrum.

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Origin of Symmetries

Cited by 168 publications

References 0 publications

Emergence of special and doubly special relativity

Emergence of special and doubly special relativity

Topological Fermi arcs in superfluid3He

Neutrino masses and mixings from an anomaly free SMG×U(1)2 model

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