arXiv subjects

J. M. Gracia-Bondía

Publications and source records attributed to J. M. Gracia-Bondía.

3 recordsLinked to original sources

arXiv2003

Moyal Planes are Spectral Triples

Axioms for nonunital spectral triples, extending those introduced in the unital case by Connes, are proposed. As a guide, and for the sake of their importance in noncommutative quantum field theory, the spaces $\R^{2N}$ endowed with Moyal products are intensively investigated. Some physical applications, such as the construction of noncommutative Wick monomials and the computation of the Connes--Lott functional action, are given for these noncommutative hyperplanes.

hep-th↗

arXiv1995

Anomaly Cancellation and gauge group of the standard model in NCG

It is well known that anomaly cancellation {\it almost} determines the hypercharges in the standard model. A related (and somewhat more stronger) phenomenon takes place in Connes' NCG framework: unimodularity (a technical condition on elements of the algebra) is {\it strictly} equivalent to anomaly cancellation (in the absence of right-handed neutrinos); and this in turn reduces the symmetry group of the theory to the standard $SU(3)\times SU(2) \times U(1)$.

hep-th↗

arXiv1994

A Renormalization Group Analysis of the NCG constraints $m_{top} = 2\,m_W}$, $m_{Higgs} = 3.14 \, m_W$

We study the evolution under the renormalization group of the restrictions on the parameters of the standard model coming from Non-Commutative Geometry, namely $m_{top} = 2\,m_W$ and $m_{Higgs} = 3.14 \, m_W$. We adopt the point of view that these relations are to be interpreted as {\it tree level} constraints and, as such, can be implemented in a mass independent renormalization scheme only at a given energy scale $μ_0$. We show that the physical predictions on the top and Higgs masses depend weakly on $μ_0$.

hep-th↗