arXiv subjects

Michael Rios

Publications and source records attributed to Michael Rios.

21 records · Page 2Linked to original sources

arXiv2005

The Geometry of Jordan Matrix Models

We elucidate the geometry of matrix models based on simple formally real Jordan algebras. Such Jordan algebras give rise to a nonassociative geometry that is a generalization of Lorentzian geometry. We emphasize constructions for the exceptional Jordan algebra and the exceptional Jordan C*-algebra and describe the projective spaces related to the exceptional cubic matrix model and the E_6 matrix model. The resulting projective spaces are shown to be exceptional versions of projective twistor space, thus revealing the existence of exceptional twistor string theories that are dual to octonionic matrix models.

math-ph↗

arXiv2005

A Jordan GNS Construction for the Holonomy-Flux *-algebra

The holonomy-flux *-algebra was recently proposed as an algebra of basic kinematical observables for loop quantum gravity. We show the conventional GNS construction breaks down when the the holonomy-flux *-algebra is allowed to be a Jordan algebra of observables. To remedy this, we give a Jordan GNS construction for the holonomy-flux *-algebra that is based on trace. This is accomplished by assuming the holonomy-flux *-algebra is an algebra of observables that is also a Banach algebra, hence a JB algebra. We show the Jordan GNS construction produces a state that is invariant under all inner derivations of the holonomy-flux *-algebra. Implications for the corresponding Jordan-Schrodinger equation are also discussed.

gr-qc↗

arXiv2005

Grassmann Variables in Jordan Matrix Models

Here we demonstrate the emergence of Grassmann variables in matrix models based on the exceptional Jordan algebra. The Grassmann algebras are built naturally using the octonion algebra. We argue the appearance of Grassmann variables solidifies the relationship between supersymmetry and triality.

hep-th↗