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

  title={Fermion Hilbert space and fermion doubling in the noncommutative geometry approach to gauge theories},
  author={Fedele Lizzi and Gianpiero Mangano and Gennaro Miele and Giovanni Sparano},
  journal={Physical Review D},
In this paper we study the structure of the Hilbert space for the recent noncommutative geometry models of gauge theories. We point out the presence of unphysical degrees of freedom similar to the ones appearing in lattice gauge theories (fermion doubling). We investigate the possibility of projecting out these states at the various levels in the construction, but we find that the results of these attempts are either physically unacceptable or geometrically unappealing. {copyright} {ital 1997… 

Noncommutative Geometry and Particle Physics

  • F. Lizzi
  • Physics
    Proceedings of Corfu Summer Institute 2017 "Schools and Workshops on Elementary Particle Physics and Gravity" — PoS(CORFU2017)
  • 2018
We review the noncommutative approach to the standard model. We start with the introduction if the mathematical concepts necessary for the definition of noncommutative spaces, and manifold in

Internal Space for the Noncommutative Geometry Standard Model and Strings

In this paper I discuss connections between the noncommutative geometry approach to the standard model on one side, and the internal space coming from strings on the other. The standard model in

The supersymmetric Yang–Mills theory on noncommutative geometry

Recently, we found the supersymmetric counterpart of the spectral triple. When we restrict the representation space to the fermionic functions of matter fields, the counterpart which we name "the

The Standard model within noncommutative geometry: a comparison of models

Algebraic Yang-Mills-Higgs theories based on noncommutative geometry have brought forth novel extensions of gauge theories with interesting applications to phenomenology. We sketch the model of

Quantum Isometries of the Finite Noncommutative Geometry of the Standard Model

We compute the quantum isometry group of the finite noncommutative geometry F describing the internal degrees of freedom in the Standard Model of particle physics. We show that this provides genuine

Supersymmetry and noncommutative geometry Part III: The noncommutative supersymmetric Standard Model

In a previous paper we developed a formalism to construct (potentially) supersymmetric theories in the context of noncommutative geometry. We apply this formalism to explore the existence of a

Noncommutative geometry, Grand Symmetry and twisted spectral triple

In the noncommutative geometry approach to the standard model we discuss the possibility to derive the extra scalar field sv - initially suggested by particle physicist to stabilize the electroweak

Spectral action and the electroweak θ-terms for the Standard Model without fermion doubling

We compute the leading terms of the spectral action for a noncommutative geometry model that has no fermion doubling. The spectral triple describing it, which is chiral and allows for CP-symmetry



The Spectral Action Principle

Abstract:We propose a new action principle to be associated with a noncommutative space . The universal formula for the spectral action is where is a spinor on the Hilbert space, is a scale and a

Noncommutative Geometry

Noncommutative Spaces It was noticed a long time ago that various properties of sets of points can be restated in terms of properties of certain commutative rings of functions over those sets. In

On the universal Chamseddine–Connes action. I. Details of the action computation

We give a detailed computation of the bosonic action of the Chamseddine–Connes model which we performed using different techniques.

Invariance Theory

  • A. Salden
  • Mathematics
    Gaussian Scale-Space Theory
  • 1997

Invariance Theory Heat Equation and Atiyah Singer Index Theorem

Pseudo-Differential Operators Introduction Fourier Transform and Sobolev Spaces Pseudo-Differential Operators on Rm Pseudo-Differential Operators on Manifolds Index of Fredholm Operators Elliptic

J. Geom. Phys

  • J. Geom. Phys
  • 1993

Gravity coupled with matter and Foundations of Geometry, hep- th/9603053

  • Gravity coupled with matter and Foundations of Geometry, hep- th/9603053


  • Phys. (Proc. Suppl.) B18
  • 1990

J. Math. Phys

  • J. Math. Phys
  • 1995