相关论文: Fermionic spectral action and the origin of nonzer…

We review the approach to the standard model of particle interactions based on spectral noncommutative geometry. The paper is (nearly) self-contained and presents both the mathematical and phenomenological aspects. In particular the bosonic…

We propose the extension of the spectral action principle to fermions and show that the neutrino mass terms appear then naturally as next-order corrections.

The presence of chiral fermions in the physical Hilbert space implies consistency conditions on the spectral action. These conditions are equivalent to the absence of gauge and gravitational anomalies. Suggestions for the fermionic part of…

We show how (a slight modification of) the noncommutative geometry bosonic spectral action can be obtained by the cancelation of the scale anomaly of the fermionic action. In this sense the standard model coupled with gravity is induced by…

A proposal that the bosonic action of gravity and the standard model is induced from the fermionic action is investigated. It is suggested that this might occur naturally in state sum models.

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…

We consider aspects of the noncommutative approach to the standard model based on the spectral action principle. We show that as a consequence of the incorporation of the Clifford structures in the formalism, the spectral action contains an…

A short introduction on elements of noncommutative geometry, which offers a purely geometric interpretation of the Standard Model and implies a higher derivative gravitational theory, is presented. Physical consequences of almost…

The principles of noncommutative geometry impose severe restrictions on the structure of (almost) commutative field theories. The Standard Model fits surprisingly well into the noncommutative framework. Here we overview some universal…

The definition of the spectral action involves the trace operator over states in the physical Hilbert space. We show that in the presence of chiral fermions there are consistency conditions on the fermionic representations. These conditions…

Starting from a theory of fermions moving in a fixed gauge and gravitational background we implement the scale invariance of the theory. Upon quantization the theory is anomalous but the anomaly can be cancelled by the addition of another…

The goal of these lectures is to present the few fundamentals of noncommutative geometry looking around its spectral approach. Strongly motivated by physics, in particular by relativity and quantum mechanics, Chamseddine and Connes have…

I will summarize Noncommutative Geometry Spectral Action, an elegant geometrical model valid at unification scale, which offers a purely gravitational explanation of the Standard Model, the most successful phenomenological model of particle…

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 particular. This defines the framework of…

The derivation of the full Standard Model from noncommutative geometry has been a promising sign for possible applications of the latter in High Energy Physics. Many believe, however, that the Standard Model cannot be the final answer. We…

A supersymmetric theory in two-dimensions has enough data to define a noncommutative space thus making it possible to use all tools of noncommutative geometry. In particular, we apply this to the N=1 supersymmetric non-linear sigma model…

We study spectral action for Riemannian manifolds with boundary, and then generalize this to noncommutative spaces which are products of a Riemannian manifold times a finite space. We determine the boundary conditions consistent with the…

In this work we present a common framework for neutrino mass and dark matter. Specifically, we work with a local $\mathcal{B-L}$ extension of the standard model which has three right-handed neutrinos, $n_{R_{i}}$, and some extra scalars,…

Neutrinos allow for a test of the hypothesis that the fermions of the Standard Model have Fermi-point splitting, analogous to the fermionic quasi-particles of certain condensed-matter systems. If present, the corresponding Lorentz-violating…

The spectral relations for the four-time fermionic Green's functions are derived in the most general case. The terms which correspond to the zero-frequency anomalies, known before only for the bosonic Green's functions, are separated and…