We review the question of whether the fundamental laws of nature limit our ability to probe
arbitrarily short distances. First, we examine what insights can be gained from thought …

A pedagogical and self-contained introduction to noncommutative quantum field theory is
presented, with emphasis on those properties that are intimately tied to string theory and …

Horizon-scale images of black holes (BHs) and their shadows have opened an
unprecedented window onto tests of gravity and fundamental physics in the strong-field …

To answer some issues raised about the concept of fractional differentiation and integration
based on the exponential and Mittag-Leffler laws, we present, in this paper, fundamental …

We propose spacetime uncertainty relations motivated by Heisenberg's uncertainty principle
and by Einstein's theory of classical gravity. Quantum spacetime is described by a non …

We present the state of the art regarding the relation between the physics of Quantum Black
Holes and Noncommutative Geometry. We start with a review of models proposed in the …

The present chapter is purely mathematical. The reader, who is more interested in physics
than mathematics can omit this chapter and go directly to Chapter 4, where the formalism of …

These lecture notes are an introduction to several ideas and applications of noncommutative
geometry. It starts with a not necessarily commutative but associative algebra which is …

We introduce the notion of real structure in our spectral geometry. This notion is motivated by
Atiyah's KR-theory and by Tomita's involution J. It allows us to remove two unpleasant …

Studies in string theory and quantum gravity suggest the existence of a finite lower limit Δ x 0
to the possible resolution of distances, at the latest on the scale of the Planck length of 10 …