Fermion Hilbert space and fermion doubling in the noncommutative geometry approach to gauge theories

Lizzi, Fedele; Mangano, G.; Miele, Gennaro; Sparano, Giovanni

doi:10.1103/physrevd.55.6357

Cited by 90 publications

(119 citation statements)

References 10 publications

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“…In this respect, it is important to understand the connection between chiral anomalies and the unimodularity conditions and we refer to [7] and [46]. In fact we shall discuss below in §9.1 the meaning of this unimodularity condition.…”

mentioning

confidence: 99%

Noncommutative geometry as a framework for unification of all fundamental interactions including gravity. Part I.

Chamseddine

Connes

2010

Fortschritte der Physik

132

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We examine the hypothesis that space-time is a product of a continuous four-dimensional manifold times a finite space. A new tensorial notation is developed to present the various constructs of noncommutative geometry. In particular, this notation is used to determine the spectral data of the standard model. The particle spectrum with all of its symmetries is derived, almost uniquely, under the assumption of irreducibility and of dimension 6 modulo 8 for the finite space. The reduction from the natural symmetry group SU (2) × SU (2) × SU (4) to U (1) × SU (2) × SU (3) is a consequence of the hypothesis that the two layers of space-time are finite distance apart but is non-dynamical. The square of the Dirac operator, and all geometrical invariants that appear in the calculation of the heat kernel expansion are evaluated. We re-derive the leading order terms in the spectral action. The geometrical action yields unification of all fundamental interactions including gravity at very high energies. We make the following predictions: (i) The number of fermions per family is 16. There is a right-handed neutrino with a see-saw mechanism. Moreover, the zeroth order spectral action obtained with a cut-off function is consistent with experimental data up to few percent. We discuss a number of open issues. We prepare the ground for computing higher order corrections since the predicted mass of the Higgs field is quite sensitive to the higher order corrections. We speculate on the nature of the noncommutative space at Planckian energies and the possible role of the fundamental group for the problem of generations.

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mentioning

confidence: 99%

Noncommutative geometry as a framework for unification of all fundamental interactions including gravity. Part I.

Chamseddine

Connes

2010

Fortschritte der Physik

132

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“…whereμ is an integration (dimensionful) constant. Finally we obtain from (A.11) and (A.9) (as we expected): 12) with some (undefined at this stage) constant γ. We emphasize, that the potential V given by (A.11) has a local minimum atÃ < 0,B > 0, but after averaging over dilatations the minimum disappears.…”

Section: Discussionmentioning

confidence: 99%

“…The writing of the fermionic action in this form (as a Pfaffian) is instrumental in the solution of the fermion doubling problem in Connes approach to the standard model [12,13,4]. In order to regularize the expression (3.4) we need to introduce a cutoff scale, which we call Λ.…”

Section: Weyl Invariance and The Fermionic Actionmentioning

confidence: 99%

Spectral action, Weyl anomaly and the Higgs-dilaton potential

Andrianov

Kurkov

Lizzi

2011

J. High Energ. Phys.

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We show how the bosonic spectral action emerges from the fermionic action by the renormalization group flow in the presence of a dilaton and the Weyl anomaly. The induced action comes out to be basically the Chamseddine-Connes spectral action introduced in the context of noncommutative geometry. The entire spectral action describes gauge and Higgs fields coupled with gravity. We then consider the effective potential and show, that it has the desired features of a broken and an unbroken phase, with the roll down.

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“…The final model has problems, notably unrealistic mass relations [78] and a disturbing fermion doubling, the removal of which causes the loss of degrees of freedom [74]. It is worth mentioning that while the standard model can be obtained from noncommutative geometry, most model of the Yang-Mills-Higgs type cannot [97,57,73].…”

Section: The Bosonic Part Of the Standard Modelmentioning

confidence: 99%

An Introduction to Noncommutative Spaces and their Geometries

Landi¹

1997

Lecture Notes in Physics

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Fermion Hilbert space and fermion doubling in the noncommutative geometry approach to gauge theories

Cited by 90 publications

References 10 publications

Noncommutative geometry as a framework for unification of all fundamental interactions including gravity. Part I.

Noncommutative geometry as a framework for unification of all fundamental interactions including gravity. Part I.

Spectral action, Weyl anomaly and the Higgs-dilaton potential

An Introduction to Noncommutative Spaces and their Geometries

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