Hilbert's Incompleteness, Chaitin's $\Omega$ number and Quantum Physics

Abstract

To explore the limitation of a class of quantum algorithms originally proposed for the Hilbert's tenth problem, we consider two further classes of mathematically non-decidable problems, those of a modified version of the Hilbert's tenth problem and of the computation of the Chaitin's $\Omega$ number, which is a representation of the Gödel's Incompletness theorem. Some interesting connection to Quantum Field Theory is pointed out.

Clarification and new references added