39 citations · 210 across the 12 of their papers we have counts for
12 papers
Incompatible coordinate algebra representations as the origin of particle generations
Shane Farnsworth
The success of the Higgs mechanism in the standard model has led to the speculation that the standard model gauge group might arise through an analogous breaking of a yet more unif…
The geometry of physical observables
Shane Farnsworth
Jordan algebras were first introduced in an effort to restructure quantum mechanics purely in terms of physical observables. In this paper we explain why, if one attempts to reform…
The standard model, the Pati-Salam model, and "Jordan geometry"
Latham Boyle, Shane Farnsworth
We argue that the ordinary commutative-and-associative algebra of spacetime coordinates (familiar from general relativity) should perhaps be replaced, not by a noncommutative algeb…
Lorentz signature and twisted spectral triples
Agostino Devastato, Shane Farnsworth, Fedele Lizzi +1
We show how twisting the spectral triple of the Standard Model of elementary particles naturally yields the Krein space associated with the Lorentzian signature of spacetime. We di…
Spinor driven cosmic bounces and their cosmological perturbations
Shane Farnsworth, Jean-Luc Lehners, Taotao Qiu
When coupling fermions to gravity, torsion is naturally induced. We consider the possibility that fermion bilinears can act as a source for torsion, altering the dynamics of the ea…
The Wavefunction of Anisotropic Inflationary Universes With No-Boundary Conditions
Sebastian F. Bramberger, Shane Farnsworth, Jean-Luc Lehners
We study the emergence of anisotropic (Bianchi IX) inflationary universes with no-boundary conditions in the path integral approach to quantum gravity. In contrast to previous work…
The graded product of real spectral triples
Shane Farnsworth
Forming the product of two geometric spaces is one of the most basic operations in geometry, but in the spectral-triple formulation of non-commutative geometry, the standard prescr…
A new algebraic structure in the standard model of particle physics
Latham Boyle, Shane Farnsworth
We introduce a new formulation of the real-spectral-triple formalism in non-commutative geometry (NCG): we explain its mathematical advantages and its success in capturing the stru…
Rethinking Connes' approach to the standard model of particle physics via non-commutative geometry
Shane Farnsworth, Latham Boyle
Connes' non-commutative geometry (NCG) is a generalization of Riemannian geometry that is particularly apt for expressing the standard model of particle physics coupled to Einstein…
Non-Commutative Geometry, Non-Associative Geometry and the Standard Model of Particle Physics
Latham Boyle, Shane Farnsworth
Connes' notion of non-commutative geometry (NCG) generalizes Riemannian geometry and yields a striking reinterepretation of the standard model of particle physics, coupled to Einst…
Non-Associative Geometry and the Spectral Action Principle
Shane Farnsworth, Latham Boyle
Chamseddine and Connes have argued that the action for Einstein gravity, coupled to the SU(3)\times SU(2)\times U(1) standard model of particle physics, may be elegantly recast as…
The Minimal Dimensionless Standard Model (MDSM) and its Cosmology
Latham Boyle, Shane Farnsworth, Joseph Fitzgerald +1
Consider the minimal renormalizable extension of the Standard Model with purely dimensionless couplings, successful electroweak symmetry breaking (via the Coleman-Weinberg mechanis…