In this introductory review, we argue that a quantum structure of space-time naturally entails
a higher-spin theory, to avoid significant Lorentz violation. A suitable framework is provided …

By a quantum metric space we mean a $ C DEGREES* $-algebra (or more generally an
order-unit space) equipped with a generalization of the usual Lipschitz seminorm on …

We study in detail generalized 4-dimensional fuzzy spheres with twisted extra dimensions.
These spheres can be viewed as $ SO (5) $-equivariant projections of quantized coadjoint …

A bstract We study perturbations of 4-dimensional fuzzy spheres as backgrounds in the IKKT
or IIB matrix model. Gauge fields and metric fluctuations are identified among the excitation …

A bstract We discuss a (3+ 1)-dimensional covariant quantum space-time describing a
FLRW cosmology with Big Bounce, obtained by a projection of the fuzzy hyperboloid H 4 n …

A bstract We present a systematic organization of functions and operators on the fuzzy 2-
sphere in terms of string modes, which are optimally localized in position and momentum …

We describe scalar and spinor fields on a noncommutative sphere starting from canonical
realizations of the enveloping algebra AU (u (2)). The gauge extension of a free spinor …

Refining previous work by Iso, Kawai and Kitazawa, we discuss bi-local string states as a
tool for loop computations in noncommutative field theory and matrix models. Defined in …

Building on mathematical structures familiar from quantum mechanics, this book provides an
introduction to quantization in a broad context before developing a framework for quantum …

We show how to make precise the vague idea that for compact metric spaces that are close
together for Gromov–Hausdorff distance, suitable vector bundles on one metric space will …