Recent results on UV-regularisation through UV-modified uncertainty relations

TL;DR

This paper reviews recent findings on UV-regularisation in quantum gravity, focusing on how UV-modified uncertainty relations can lead to a finite lower bound on position uncertainty, affecting the structure of spacetime.

Contribution

It introduces a new perspective on UV-regularisation via UV-modified uncertainty relations, highlighting a mechanism that converts lost external degrees of freedom into internal ones.

Findings

UV-regularity in short distance structures

Classification of possible short distance geometries

A mechanism for internalizing degrees of freedom

Abstract

Assume that in a fundamental theory of quantum gravity spatial information is encoded through elements x_i of an associative, complex and possibly noncommutative algebra in which the involution acts as x^*_i = x_i. Without further assumptions it can be shown that such x_i can describe only three different types of short distance structures: I. a lattice, II. a continuum or III. a finite lower bound on the uncertainty in positions, as e.g. described in a stringy uncertainty relation. All other cases are mixtures of the three. We briefly review recent results on the case III short distance structure, in particular its ultraviolet regularity and a possible new mechanism that turns the external degrees of freedom lost through the UV-cutoff into internal degrees of freedom.